References
Published online by Cambridge University Press: 05 December 2015
Summary
A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
- Type
- Chapter
- Information
- Unit Equations in Diophantine Number Theory , pp. 337 - 357Publisher: Cambridge University PressPrint publication year: 2015
References
and (2012), On vanishing coefficients of algebraic power series over fields of positive characteristic, Invent. Math. 187, 343–393.CrossRefGoogle Scholar
(1999), The set of solutions of a polynomial-exponential equation, Acta Arith. 87, 189–207.CrossRefGoogle Scholar
(2007),On the multiplicity of linear recurrence sequences, J. Number Theory 126, 212–216.CrossRefGoogle Scholar
and (2009), Small points on subvarieties of a torus, Duke Math. J. 150, 407–442.CrossRefGoogle Scholar
and (2011), On the zeros of linear recurrence sequences, Acta Arith. 147 (2011), 387–396.CrossRefGoogle Scholar
, and (2008), Ledrappier's system is almost mixing of all orders, Ergodic Theory Dynam. Systems 28, 339–365.CrossRefGoogle Scholar
(2004), Ideal membership in polynomial rings over the integers, J. Amer. Math. Soc. 17, 407–442.CrossRefGoogle Scholar
(1966), Linear forms in the logarithms of algebraic numbers, Mathematika 13, 204–216.CrossRefGoogle Scholar
(1967a), Linear forms in the logarithms of algebraic numbers, II, Mathematika 14, 102–107.Google Scholar
(1967b), Linear forms in the logarithms of algebraic numbers, III, Mathematika 14, 220–228.Google Scholar
(1968a), Linear forms in the logarithms of algebraic numbers, IV, Mathematika 15, 204–216.CrossRefGoogle Scholar
(1968b), Contributions to the theory of Diophantine equations, Philos. Trans. Roy. Soc. London, Ser. A 263, 173–208.Google Scholar
(1968c), The Diophantine equation y2 = ax3 + bx2 + cx + d, J. London Math. Soc. 43, 1–9.Google Scholar
(1969), Bounds for the solutions of the hyperelliptic equation, Proc. Camb. Philos. Soc. 65, 439–444.CrossRefGoogle Scholar
, ed. (1988), New Advances in Transcendence Theory, Cambridge University Press.CrossRefGoogle Scholar
(1998), Logarithmic forms and the abc-conjecture, in: Number Theory Diophantine, Computational and AlgebraicAspects, Proc. Conf. Eger, 1966, , and , eds., de Gruyter, 37–44.Google Scholar
and (1969), The equations 3x2 - 2 = y2 and 8x2 - 7 = z2, Quart. J. Math. Oxford Ser. (2) 20, 129–137.CrossRefGoogle Scholar
and , eds. (1977), Transcendence theory: advances and applications, Academic Press.
, and (2011), Additive unit representations in rings over global fields – a survey, Publ. Math. Debrecen 79, 291–307.Google Scholar
(1974), Integers expressible as sums of distinct units, Bull. London Math. Soc. 6, 66–68.CrossRefGoogle Scholar
(2013), Representing integers as sums or differences of general power products, Acta Math. Hungar. 141, 291–300.CrossRefGoogle Scholar
(2000), On the number of solutions of index form equations, Publ. Math. Debrecen 56, 251–262.Google Scholar
(2015a), Effective results for unit points over finitely generated domains, Math. Proc. Camb. Phil. Soc. 158, 331–353.CrossRefGoogle Scholar
(2015b), Effective results for division points on curves in G2m, J. Th.Nombers Bordeaux, to appear.
, and (2004), On the number of equivalence classes of binary forms of given degree and given discriminant, Acta Arith. 113, 363–399.CrossRefGoogle Scholar
, and (2007a), On the number of pairs of binary forms with given degree and given resultant, Acta Arith. 128, 19–54.CrossRefGoogle Scholar
, and (2007b), Diophantine problems related to discriminants and resultants of binary forms, in: Diophantine Geometry, proceedings of a trimester held from April–July 2005, , ed., CRM series, Scuola Normale Superiore Pisa, pp. 45–63.Google Scholar
, and (2009), Effective results for linear equations in two unknowns from a multiplicative division group, Acta Arith. 136, 331–349.CrossRefGoogle Scholar
, and (2013), Multiply monogenic orders, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 12, 467–497.Google Scholar
, and (2014), Effective results for Diophantine equations over finitely generated domains, Acta Arith. 163, 71–100.CrossRefGoogle Scholar
, , and (2009), Effective results for points on certain subvarieties of a tori, Math. Proc. Camb. Phil. Soc. 147, 69–94.CrossRefGoogle Scholar
and (2002), On the number of solutions of decomposable polynomial equations, Acta Arith. 101, 171–187.CrossRefGoogle Scholar
and (1996), The equation x + y = 1 in finitely generated groups, Acta. Arith. 78, 189–199.CrossRefGoogle Scholar
and (1997), Lower bounds of heights of points on hypersurfaces, Acta Arith. 79, 103–111.CrossRefGoogle Scholar
(1995), Effective analysis of integral points on algebraic curves, Israel J. Math. 90, 235–252.CrossRefGoogle Scholar
(2002), Baker's method and modular curves, in: A Panorama of Number Theory, or The View from Baker's Garden, Proc. conf. ETH Zurich, 1999, , ed., Cambridge University Press, pp. 73–88.Google Scholar
(2008), The many faces of the subspace theorem [after Adamczewski, Bugeaud, Corvaja, Zannier, . . .], Séminaire Bourbaki, Vol. 2006/2007, Astérisque 317, Exp. No. 967, vii, 1–38.Google Scholar
and (2000), Démonstration du théor`eme de Baker-Feldman via les formes linéaires en deux logarithmes, J. Théorie des Nombres, Bordeaux, 12, 13–23.CrossRefGoogle Scholar
, and (2004), Index form equations in sextic fields: a hard computation, Acta Arith. 115, 85–96.CrossRefGoogle Scholar
and (1996), Solving Thue equations of high degree, J. Number Theory, 60, 373–392.CrossRefGoogle Scholar
and (1998), Solving superelliptic Diophantine equations by Baker's method, Compositio Math. 112, 273–312.CrossRefGoogle Scholar
and (1972), Finiteness theorems for binary forms with given discriminant, Proc. London Math. Soc. 24, 385–394.Google Scholar
(1993), Effective diophantine approximation on GM, Ann. Scuola Norm. Sup. Pisa (IV) 20, 61–89.Google Scholar
and (1997), Effective Diophantine approximation on Gm, II, Ann. Scuola Norm. Sup. Pisa (IV) 24, 205–225.Google Scholar
and (2003), An elementary approach to effective Diophantine approximation on Gm, in Number Theory and Algebraic Geometry, To Peter Swinaerton Dyer on his 75th birthday, London Math. Soc. Lecture Note Series 303, and , eds. Cambridge University Press, pp. 41–62.Google Scholar
, and (1997), The unit equation and the cluster principle, Acta Arith. 79, 361–389.CrossRefGoogle Scholar
, and (2001), Equations in one variable over function fields, Acta Arith. 99, 27–39.CrossRefGoogle Scholar
, , and (1989), A sharp bound for solutions of linear Diophantine equations, Proc. Amer. Math. Soc. 105, 844–846.CrossRefGoogle Scholar
, and (1997), The Magma algebra system I. The user languange, J. Symbolic Comput, 24, 235–265.CrossRefGoogle Scholar
(1984), On S-integral solutions of the equation ym = f (x), Acta Math. Hungar. 44, 133–139.CrossRefGoogle Scholar
and (1990), On unit equations with rational coefficients, Acta Arith. 53, 367–388.CrossRefGoogle Scholar
(1999), Some examples related to the abc-conjecture for algebraic number fields, Math. Comp. 69, 1707–1710.CrossRefGoogle Scholar
and (1986), Vanishing sums in function fields, Math. Soc. Camb. Phil. Soc. 100, 427–434.Google Scholar
, and (2006), Bases of canonical number systems in quartic number fields, J. Théor. Nombres Bordeaux 18, 537–557.CrossRefGoogle Scholar
(1998), Bornes effectives pour les solutions des équations en S-unités et des équations de Thue-Mahler, J. Number Theory 71, 227–244.CrossRefGoogle Scholar
(2011), Quantitative versions of the subspace theorem and applications, J. Théor. Nombres Bordeaux 23, 35–57.CrossRefGoogle Scholar
(2012), Distribution Modulo One and Diophantine Approximation, Cambridge Tracts in Mathematics 193, Cambridge University Press.Google Scholar
and (1996a), Bounds for the solutions of unit equations, Acta Arith. 74, 67–80.CrossRefGoogle Scholar
and (1996b), Bounds for the solutions of Thue-Mahler equations and norm form equations, Acta Arith. 74, 273–292.CrossRefGoogle Scholar
and (2004), A quantitative lower bound for the greatest prime factor of (ab + 1)(bc + a)(ca + 1), Acta Arith. 114, 275–294.CrossRefGoogle Scholar
and (1980), Über algebraische Unabhängigkeit bei gewissen nichtfortsetzbaren Potenzreihen, Arch. Math. 34, 32–36.CrossRefGoogle Scholar
(2007), Finite orbits for rational functions, Indag. Mathem., N.S. 18, 203–214.CrossRefGoogle Scholar
and (1973), On the transcendence of certain power series of algebraic numbers, Acta Arith. 23, 301–305.CrossRefGoogle Scholar
(1969), An effective p-adic analogue of a theorem of Thue, Acta Arith. 15, 279–305.CrossRefGoogle Scholar
(1970), An effective p-adic analogue of a theorem of Thue II, The greatest prime factor of a binary form, Acta Arith, 16, 392–412.CrossRefGoogle Scholar
and (1976), Trigonometric Diophantine equations (on vanishing sums of roots of unity), Acta Arith. 30, 229–240.CrossRefGoogle Scholar
, and (2010), The Diophantine equation αx11 · · · αxnn = f (x1, . . ., xn) II, Trans. Amer. Math. Soc. 362, 2115–2123.Google Scholar
and (2002a), A subspace theorem approach to integral points on curves, C.R. Math. Acad. Sci. Paris 334, 267–271.CrossRefGoogle Scholar
and (2002b), Some new applications of the subspace theorem, Compos. Math. 131, 319–340.CrossRefGoogle Scholar
and (2003), On the greatest prime factor of (ab + 1)(ac + 1), Proc. Amer. Math. Soc. 131, 1705–1709.CrossRefGoogle Scholar
and (2006), On the integral points on certain surfaces, Int. Math. Res. Not. Art.ID 98623, 20 pp.Google Scholar
and (2008), Applications of the Subspace Theorem to certain Diophantine problems: a survey of some recent results, in: Diophantine Approximation, Festschrift for Wolfgang Schmidt, , and , eds., Springer Verlag, pp. 161–174.Google Scholar
and (1999), Minorations des hauteurs normalisées des sousvari étés des tores, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 28, 489–543, Errata, 29, 729–731.Google Scholar
(1930), Über die Darstellung der Zahlen durch die binären kubischen Formen von negativer Diskriminante, Math. Z, 31, 1–26.Google Scholar
and (1940), The theory of irrationalities of the third degree (Russian), Inst. Math. Steklov 11, Acad. Sci. USSR. English translation, Amer. Math. Soc., 1964.
(2007), A Skolem-Mahler-Lech theorem in positive characteristic and finite automata, Invent. Math. 168, 175–244.CrossRefGoogle Scholar
and (2012), Linear equations over multiplicative groups, recurrences, and mixing I, Proc. London Math. Soc. 104, 1045–1083.CrossRefGoogle Scholar
, and (2014), Representing algebraic integers as linear combinations of units, Period. Math. Hung. 68, 135–142.CrossRefGoogle Scholar
and (1975) Approximation rationnelles simultanées de nombres algébriques réels et de nombres algébriques p-adiques, in: Journées Arithmétiques de Bordeaux (Conf. Univ. Bordeaux, 1974), , ed., Astérisque 24/25, Soc. Math. France, pp. 211–227.Google Scholar
and (1976), Sur la majoration de formes linéaires à coefficients algébriques réels et p-adiques. Démonstration d'une conjecture de K. Mahler, C.R. Acad. Sci. Paris Sér. A-B 282, A1211–A1214.Google Scholar
(1947), The approximation of algebraic numbers by rationals, Acta Math. 79, 225–240.CrossRefGoogle Scholar
(1966), Introduction to the theory of algebraic numbers and functions, Academic Press.Google Scholar
(1976), Problems in number theory and combinatorics, Proc. 6th Manitoba Conference on Numerical Math. pp. 35–58.Google Scholar
, and (1988), Some Diophantine equations with many solutions, Compos. Math. 66, 37–56.Google Scholar
and (1934), On a problem in the elementary theory of numbers, Amer. Math. Monthly 41, 608–611.CrossRefGoogle Scholar
and (1997), Counting solutions of decomposable form equations, Acta Arith. 79, 173–191.CrossRefGoogle Scholar
(1983), Upper bounds for the numbers of solutions of Diophantine equations,Ph.D. thesis, University of Leiden, Leiden. Also published as Math. Centre Tracts No. 168, CWI, Amsterdam.Google Scholar
(1984a), On equations in S-units and the Thue-Mahler equation, Invent. Math. 75, 561–584.CrossRefGoogle Scholar
(1995), The number of solutions of decomposable form equations, Invent. Math. 122, 559–601.CrossRefGoogle Scholar
(1996), An improvement of the quantitative subspace theorem, Compos. Math. 101, 225–311.Google Scholar
(1997), The number of solutions of the Thue-Mahler equation, J. Reine Angew. Math. 482, 121–149.Google Scholar
(1998), Lower bounds for resultants, II, in: Number Theory, Diophantine, Computational and Algebraic Aspects, Proc. Conf. Eger, Hungary, 1996, , , , eds., Walter de Gruyter, pp. 181–198.Google Scholar
(1999), The number of solutions of linear equations in roots of unity, Acta Arith. 89, 45–51.CrossRefGoogle Scholar
(2002), Points on subvarieties of tori, in: A Panorama of Number Theory, or the View from Baker's Garden, Proc. conf. ETH Zürich, 1999, , ed., Cambridge University Press, pp. 214–230.Google Scholar
(2004), Linear equations with unknowns from a multiplicative group whose solutions lie in a small number of subspaces, Indag. Math. (N.S.) 15, 347–355.CrossRefGoogle Scholar
and (2002), Diophantine inequalities on projective varieties, Int. Math. Res. Not. 2002:25, 1295–1130.Google Scholar
and (2008), A generalization of the Subspace Theorem with polynomials of higher degree, in: Diophantine Approximation, Festschrift for Wolfgang Schmidt, , and , eds., Springer Verlag, pp. 175–198.Google Scholar
and (2013), A further improvement of the Quantitative Subspace Theorem, Ann. Math. 177, 513–590.CrossRefGoogle Scholar
, and (1989), On the numbers of solutions of decomposable polynomial equations, Arch. Math. 52, 337–353.CrossRefGoogle Scholar
and (1985), On unit equations and decomposable form equations, J. Reine Angew. Math. 358, 6–19.
and (1988a), On the number of polynomials and integral elements of given discriminant, Acta. Math. Hung. 51, 341–362.CrossRefGoogle Scholar
and (1988b), On the number of solutions of weighted unit equations, Compos. Math. 66, 329–354.Google Scholar
and (1988c), Finiteness criteria for decomposable form equations, Acta Arith. 50, 357–379.CrossRefGoogle Scholar
and (1988d), Decomposable form equations, in: New Advances in Transcendence Theory, Proc. conf. Durham 1986, , ed., pp. 175–202.Google Scholar
and (1989), Thue-Mahler equations with a small number of solutions, J. Reine Angew. Math. 399, 60–80.Google Scholar
and (1991), Effective finiteness results for binary forms with given discriminant, Compositio Math., 79, 169–204.Google Scholar
and (1992a), Effective finiteness theorems for decomposable forms of given discriminant, Acta. Arith. 60, 233–277.CrossRefGoogle Scholar
and (1992b), Discriminants of decomposable forms, in: New Trends in Probability and Statistics, and , eds., pp. 39–56.Google Scholar
and (1997), The number of families of solutions of decomposable form equations, Acta. Arith. 80, 367–394.CrossRefGoogle Scholar
and (2013), Effective results for unit equations over finitely generated domains, Math. Proc. Camb. Phil. Soc. 154, 351–380.CrossRefGoogle Scholar
and (2016), Discriminant Equations in Diophantine Number Theory, Cambridge: Cambridge University Press, to appear.Google Scholar
, , and (1988a), On S-unit equations in two unknowns, Invent. math. 92, 461–477.CrossRefGoogle Scholar
, , and (1988b), S-unit equations and their applications, in: New Advances in Transcendence Theory, Proc. conf. Durham 1986, , ed., pp. 110–174. Cambridge University Press.Google Scholar
, , and (2003), Multivariate equations with many solutions, Acta Arith. 107 (2003), 103–125.CrossRefGoogle Scholar
and (1999), The Absolute Subspace Theorem and linear equations with unknowns from a multiplicative group, in: Number Theory in Progress, proc. conf. Zakopane 1997 in honour of the 60th birthday of Prof., , and , eds.,Walter de Gruyter, pp. 121–142.Google Scholar
and (2002), A quantitative version of the Absolute Subspace Theorem, J. Reine Angew. Math. 548, 21–127.Google Scholar
, and (2002), Linear equations in variables which lie in a multiplicative group, Ann. Math. 155, 807–836.CrossRefGoogle Scholar
and (1986), Uniform bounds for the number of solutions to Yn = f (X), Math. Proc. Camb. Phil. Soc. 100, 237–248.CrossRefGoogle Scholar
and (2008), Linear equations with unknowns from a multiplicative group in a function field, Acta Arith. 133, volume dedicated to the 75th birthday of Wolfgang Schmidt, 157–170.Google Scholar
(1983), Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math. 73, 349–366, Erratum: Invent. Math. 75 (1984), 381.Google Scholar
(1991), Diophantine approximation on abelian varieties, Ann. Math. 133, 549–576.CrossRefGoogle Scholar
(1994), The general case of S. Lang's conjecture, in: Bersotti symposium in Algebraic Geometry (Abano Terme, 1991), 175–182, Perspect. Math. 15, Academic Press.Google Scholar
and (1994), Diophantine approximations on projective spaces, Invent. Math. 116, 109–138.CrossRefGoogle Scholar
and (1998), Transcendental numbers, Springer Verlag, Vol. 44 of Encyclopaedia of Math. Sci.Google Scholar
, and (2008), The additive unit structure of pure quartic complex fields, Funct. Approx. Comment. Math. 39, 113–131.CrossRefGoogle Scholar
and (1985), Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comp. 44, 463–471.CrossRefGoogle Scholar
(2012), On rings of integers generated by their units, Bull. London Math. Soc. 44, 167–182.CrossRefGoogle Scholar
(1989), Analytic formulas for regulators of number fields, Invent. Math. 98, 599–622.CrossRefGoogle Scholar
and (1956), Effective procedures in field theory, Philos. Trans. Roy. Soc.London, Ser. A 248, 407–432.CrossRefGoogle Scholar
(1984), Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients, Studia Sci. Math. Hungar 19, 399–411.Google Scholar
(1985), Norm form equations with several dominating variables and explicit lower bounds for inhomogeneous linear forms with algebraic coefficients, II, Studia Sci. Math. Hungar 20, 333–344.Google Scholar
(1986), Inhomogeneous discriminant form and index form equations and their applications, Publ. Math. Debrecen 33, 1–12.Google Scholar
(1988a), Integral elements with given discriminant over function fields, Acta Math. Hungar. 52, 133–146.CrossRefGoogle Scholar
(1988b), Inhomogeneous norm form equations over function fields, Acta Arith. 51, 61–73.CrossRefGoogle Scholar
and (2002), On the resolution of relative Thue equations, Math. Comp. 71, no. 237, 429–440 (electronic).Google Scholar
and (2006a), Diophantine equations over global function fields I, The Thue equation, J. Number Theory 119, 49–65.CrossRefGoogle Scholar
and (2006b), Diophantine equations over global function fields II, S-integral solutions of Thus equations, Exper. Math. 15, 1–6.CrossRefGoogle Scholar
and (2010), Diophantine equations over global function fields IV, S-unit equations in several variables with an application to norm form equations, J. Number Theory 130, 493–506.CrossRefGoogle Scholar
(1934), Sur le septième problème de Hilbert, Izv. Akad. Nauk SSSR 7, 623–630.
(1935), On approximating transcendental numbers by algebraic numbers, Dokl. Akad. Nauk SSSR 2, 177–182.Google Scholar
(1940), Sur la divisibilité de la différence des puissances de deux nombres entiers par une puissance d'un idéal premier, Mat. Sbornik 7(49), 7–26.Google Scholar
(2008), The isotrivial case in the Mordell-Lang theorem, Trans. Amer. Math. Soc. 360, 3839–3856.CrossRefGoogle Scholar
(1996), Sequences of Fields with Many Solutions to the Unit Equation, The Rocky Mountain J. Math. 26, 1017–1029.CrossRefGoogle Scholar
and (2000), abc implies no “Siegel zeros” for L-functions of characters with negative discriminant, Invent. Math. 139, 509–523.CrossRefGoogle Scholar
and (2008), The primes contain arbitrarily long arithmetic progressions, Ann. of Math. 167, 481–547.CrossRefGoogle Scholar
(1971), Sur l'irréductibilité d'une classe des polynômes, I, Publ. Math. Debrecen 18, 289–307.Google Scholar
(1972), Sur l'irréductibilité d'une classe des polynômes, II, Publ. Math. Debrecen 19, 293–326.Google Scholar
(1973), Sur les polynômes à coefficients entiers et de discriminant donné, Acta Arith. 23, 419–426.CrossRefGoogle Scholar
(1974), Sur les polynômes à coefficients entiers et de discriminant donné II, Publ. Math. Debrecen 21, 125–144.Google Scholar
(1976), Sur les polynômes à coefficients entiers et de discriminant donné III, Publ. Math. Debrecen 23, 141–165.Google Scholar
(1978a), On polynomials with integer coefficients and given discriminant IV, Publ. Math. Debrecen 25, 155–167.Google Scholar
(1978b), On polynomials with integer coefficients and given discriminant V, p-adic generalizations, Acta Math. Acad. Sci. Hung. 32, 175–190.Google Scholar
(1978/1979), On the greatest prime factors of decomposable forms at integer points, Ann. Acad. Sci. Fenn., Ser. A I, Math. 4, 341–355.Google Scholar
(1979), On the number of solutions of linear equations in units of an algebraic number field, Comment. Math. Helv. 54, 583–600.CrossRefGoogle Scholar
(1979/1980), On the solutions of linear diophantine equations in algebraic integers of bounded norm, Ann. Univ. Sci. Budapest. Eötvös, Sect. Math. 22–23, 225–233.Google Scholar
(1980a), Explicit upper bounds for the solutions of some diophantine equations, Ann. Acad. Sci. Fenn., Ser A I, Math. 5, 3–12.CrossRefGoogle Scholar
(1980b), Résultats effectifs sur la représentation des entiers par des formes désomposables, Queen's Papers in Pure and Applied Math., No.56.Google Scholar
(1980c), On certain graphs composed of algebraic integers of a number field and their applications I, Publ. Math.Debrecen 27, 229-242.Google Scholar
(1981a), On the representation of integers by decomposable forms in several variables, Publ. Math.Debrecen 28, 89–98.Google Scholar
(1981b), On S-integral solutions of norm form, discriminant form and index form equations, Studia Sci. Math.Hungar 16, 149–161.Google Scholar
(1981c), On discriminants and indices of integers of an algebraic number field, J. Reine Angew. Math. 324, 114–126.Google Scholar
(1982a), Polynomials of given discriminant and integral elements of given discriminant over integral domains, C. R. Math. Rep. Acad. Sci.Canada 4, 75–80.Google Scholar
(1982b), On certain graphs associated with an integral domain and their applications to Diophantine problems, Publ. Math.Debrecen 29, 79–94.Google Scholar
(1982c), On the irreducibility of a class of polynomials III. J. Number Theory 15, 164–181.CrossRefGoogle Scholar
(1983), Bounds for the solutions of norm form, discriminant form and index form equations in finitely generated integral domains, Acta Math. Hung. 42, 45–80.Google Scholar
(1984), Effective finiteness theorems for polynomials with given discriminant and integral elements with given discriminant over finitely generated domains, J. Reine Angew. Math. 346, 54–100.Google Scholar
(1990), On arithmetic graphs associated with integral domains, in: A Tribute to Paul Erdős, Cambridge University Press, pp. 207–222.Google Scholar
(1992b), Upper bounds for the numbers of solutions of unit equations in two unknowns, Lithuanian Math. J. 32, 40–44.CrossRefGoogle Scholar
(1992c), On the irreducibility of a class of polynomials IV, Acta Arith. 62, 399–405.CrossRefGoogle Scholar
(1993a), On the numbers of families of solutions of systems of decomposable form equations, Publ. Math.Debrecen 42, 65–101.Google Scholar
(1993b), Some applications of decomposable form equations to resultant equations, Coll. Math. 65, 267–275.Google Scholar
(1993c), On the number of pairs of polynomials with given resultant or given semi-resultant, Acta Sci. Math. 57, 515–529.Google Scholar
(1994), On the irreducibility of neighbouring polynomials, Acta. Arith. 67, 283–294.CrossRefGoogle Scholar
(1996), Applications of unit equations, in: Analytic Number Theory, RIMS Kokyusoku 958, Kyoto, Japan, pp. 62–78.Google Scholar
(1998), Bounds for the solutions of decomposable form equations, Publ. Math.Debrecen 52, 1–31.Google Scholar
(1999), On the distribution of solutions of decomposable form equations, in: Number Theory in Progress, Proc. conf. in honour of 60th birthday of , , and , eds., de Gruyter, pp. 237– 365.CrossRefGoogle Scholar
(2002), Solving diophantine equations by Baker's theory, in: A Panorama of Number Theory, Cambridge, pp. 38–72.Google Scholar
(2006), Polynomials and binary forms with given discriminant, Publ. Math.Debrecen 69, 473–499.Google Scholar
(2008a), On the abc-conjecture in algebraic number fields, Acta Arith. 133, 281–295.CrossRefGoogle Scholar
(2008b), On certain arithmetic graphs and their applications to diophantine problems, Funct. Approx. Comment. Math., 39, 289–314.CrossRefGoogle Scholar
(2010), S-unit equations in number fields: effective results, generalizations, ABC-conjecture, in: Analytic number theory and related topics, RIMS Kokyusoku 1710, pp. 71–84.Google Scholar
, and (2011), Irreducibility criteria of Schur-type and Pólya-type, Monatsh. Math. 163, 415–443.CrossRefGoogle Scholar
, and (2014), Representation of finite graphs as difference graphs of S-units, I, J. Combinatorial Theory, Ser. A, 127, 314–335.Google Scholar
and (1977), On discriminant form and index form equations, Studia Sci. Math.Hungar. 12, 47–60.Google Scholar
and (1978), Effective estimates for the integer solutions of norm form and discriminant form equations, Publ. Math.Debrecen 25, 311–325.Google Scholar
and (1980), Über die Verteilung der Lösungen von Normformen Gleichungen III, Acta Arith. 37, 143–165.CrossRefGoogle Scholar
, and (2004), Power values of polynomials and binomial Thue-Mahler equations, Publ. Math.Debrecen 65, 341–362.Google Scholar
and (2008), Polynomial powers and a common generalization of binomial Thue-Mahler equations and S-unit equations, in: Diophantine Equations, Proc. conf. in honour of Tarlok Shorey's 60th birthday, , ed., New Delhi, pp. 103–119.Google Scholar
and (1998), Integer solutions of a sequence of decomposable form inequalities, Acta Arith. 86, 227–237.CrossRefGoogle Scholar
, and (1996), On the number of prime factors of integers of the form ab + 1, Acta Arith. 74, 365–385.CrossRefGoogle Scholar
and (1994), On a conjecture of Posner and Rumsey, J. Number Theory, 47, 63–78.CrossRefGoogle Scholar
and (2006), Bounds for the solutions of S-unit equations and decomposable form equations, Acta Arith. 123, 9–41.CrossRefGoogle Scholar
(1993), A quantitative version of Dirichlet's S-unit theorem in algebraic number fields, Publ. Math. Debrecen 42, 239–246.Google Scholar
(1997), On a problem of Győry and Schinzel concerning polynomials, Acta Arith. 78, 287–295.CrossRefGoogle Scholar
(2007), Arithmetic progressions in linear combinations of S-units, Period. Math. Hung. 54, 175–181.CrossRefGoogle Scholar
(2009), Optimal systems of fundamental S-units for LLL-reduction, Periodica Math. Hung. 59, 79–105.CrossRefGoogle Scholar
and (2010), On the length of arithmetic progressions in linear combinations of S-units, Archiv Math. 94, 357–363.CrossRefGoogle Scholar
and (2003), Polynomials dividing infinitely many quadrinomials or quintinomials, Acta Arith. 107, 381–404.CrossRefGoogle Scholar
and (2008), A criterion for polynomials to divide infinitely many k-nomials, in: Diophantine Approximation, Festschrift forWolfgang Schmidt, , and , eds., Springer Verlag, pp. 175–198.Google Scholar
and (1997), Polynomial cycles and dynamical units, in: Proc. Conf. Analytic and Elementary Number Theory, dedicated to the 80th birthday of E. Hlawka, and , eds., Wien, 1997, 70–80.Google Scholar
and (1980), An introduction to the theory of numbers, 5th. edn., Oxford University Press.Google Scholar
(1926), Die Frage der endlich vielen Schritte in der Theorie der Polynomideale, Math. Ann. 95, 736–788.CrossRefGoogle Scholar
(1851), Sur l'introduction des variables continues dans la théorie des nombres, J. Reine Angew. Math. 41, 191–216.Google Scholar
and (2003), On the largest prime factor of (ab + 1)(ac + 1)(bc + 1), Bol. Soc. Mat. Mexicana, 9, 235–244.Google Scholar
(2007), Exceptional units and Euclidean number fields, Archiv Math. 88, 425–433.CrossRefGoogle Scholar
(1996), The Mordell-Lang conjecture for function fields, J. Amer. Math. Soc. 9, 667–690.Google Scholar
and (2004), The ABCtheorem for higher-dimensional function fields, Trans. Amer. Math. Soc. 356, no. 7, 2871–2887.CrossRefGoogle Scholar
(1999), On p-adic norm form inequalities, Master thesis, Leiden.
and (2011), Conjecture de Shafarevich effective pour les revêtements cycliques, Algebra and Number Theory 5, 1133–1143.
(2011), An effective proof of the hyperelliptic Shafarevich conjecture and applications, Ph.D. thesis, ETH Zürich.
(2013), On Szpiro's discriminant conjecture, Internat.Math. Res. Notices 1–35. Published online: doi:10.193/imrn/vnt079.Google Scholar
(2014a), An effective proof of the hyperelliptic Shafarevich conjecture, J. Théorie des Nombres, Bordeaux, 26, 507–530.CrossRefGoogle Scholar
(2014b) Modularity and integral points on moduli schemes, arXiv:1310.7263v2 [math.NT].
and (2007), Two S-unit equations with many solutions, J. Number Theory 124, 193–199.CrossRefGoogle Scholar
(1981), Effective bound for a linear form with algebraic coefficients in the archimedean and p-adic metrics, Inst. Math. Akad. Nauk BSSR, Preprint No. 24, Minsk (Russian).Google Scholar
and (1973), An effective analysis of the Thue-Mahler equation in relative fields, Dokl. Akad. Nauk BSSR 17, 393–395 (Russian).Google Scholar
(1981), Canonical number systems in algebraic number fields, Acta Math. Acad. Sci. Hungar. 37, 405–407.CrossRefGoogle Scholar
and (1991), Number systems in integral domains, especially in orders of algebraic number fields, Acta Sci. Math. 55, 287–299.Google Scholar
(2015), The Catalan Equation, Master thesis, Leiden University.
and (2011), Smooth solutions to the abc equation: the xyz conjecture, J. Théorie des Nombres de Bordeaux 23, 209–234.CrossRefGoogle Scholar
(1773), Recherches d'arithmétiques, Nouv.Mém. Acad. Berlin, 265–312; Oeuvres III, 693–758.Google Scholar
(1918), Verallgemeinerung eines Pólyaschen Satzes auf algebraische Zahlkörper, Nachr. Ges. Wiss. G¨ottingen, 478–488.Google Scholar
(1999), Liens entre le théorème de Mason et la conjecture (abc), in: Number Theory (5th conf. ofCNTA, OttawaON1996), and , eds. 187–213. CRM Proc. Lecture Notes 19, AMS, Providence RI.Google Scholar
(1989), Équations exponentielles polynômes et suites récurrentes linéaires, II, J. Number Theory 31, 24–53.CrossRefGoogle Scholar
(1933), Factorization of certain cyclotomic functions, Ann. Math. (2) 34, 461–479.CrossRefGoogle Scholar
(2012), Linear equations over multiplicative groups in positive characteristic, Acta Arith. 153, 325–347.CrossRefGoogle Scholar
, and (1982), Factoring polynomials with rational coefficients, Math. Ann. 261, 515–534.CrossRefGoogle Scholar
(1985), Euclidean fields having a large Lenstra constant, Ann. Inst. Fourier 35, 83–106.CrossRefGoogle Scholar
and (1989), On cliques of exceptional units and Lenstra's construction of Euclidean fields, Lecture Notes Math. 1380, 150–178.Google Scholar
and (2011), Some remarks on diophantine equations and diophantine approximation, Vietnam J. Math. 39, 343–368.Google Scholar
and (2012), Familles d’équations de Thue-Mahler n'ayant que des solutions triviales, Acta Arith. 155, 117–138.CrossRefGoogle Scholar
(2006), One-parameter families of unit equations, Math. Res. Lett. 13, 935–945.CrossRefGoogle Scholar
(2008), The dimension of integral points and holomorphic curves on the complements of hyperplanes, Acta Arith. 134, 259–270.CrossRefGoogle Scholar
(2014), Lower bounds in logarithms and integral points on higher dimensional varieties, Algebra Number Theory 8, 647–687.CrossRefGoogle Scholar
and (1961), Representation of integers by binary forms, Acta Arith. 6, 333–363.CrossRefGoogle Scholar
(2015), On p-adic Decomposable Form Inequalities, Ph.D. thesis, Leiden.
and (2004), Uniformly counting points of bounded height, Acta Arith. 111, 277–297.CrossRefGoogle Scholar
(2000), Explicit bounds for residues of Dedekind zeta functions, values of L-functions at s = 1, and relative class numbers, J. Number Theory 85, 263–282.CrossRefGoogle Scholar
and (1983), Multiplicative dependence in number fields, Acta Arith. 42, 291–302.CrossRefGoogle Scholar
(2005), On the greatest common divisor of u - 1 and v - 1 with u and v near S-units, Monatsh. Math. 146, 239–256.CrossRefGoogle Scholar
(1933a), Zur Approximation algebraischer Zahlen I: Über den gro¨ssten Primteiler binärer Formen, Math. Ann. 107, 691–730.CrossRefGoogle Scholar
(1933b), Zur Approximation algebraischer Zahlen III: Über die mittlere Anzahl grosser Zahlen durch binäre Formen, Acta Math. 62, 91–166.CrossRefGoogle Scholar
(1935a), Eine arithmetische Eigenschaft der Taylor-koeffizienten rationaler Functionen, Proc. Kon. Ned. Akad. Wetensch. 38, 50–60.Google Scholar
(1983), The hyperelliptic equation over function fields, Math. Proc. Camb. Phil. Soc. 93, 219–230.CrossRefGoogle Scholar
(1984), Diophantine equations over function fields, Cambridge University Press.CrossRefGoogle Scholar
(1986b), Norm form equations III: positive characteristic, Math. Proc. Camb. Phil. Soc. 99, 409–423.CrossRefGoogle Scholar
(1987), Norm form equations V. Degenerate modules, J. Number Theory 25, 239–248.CrossRefGoogle Scholar
(1988), The study of Diophantine equations over function fields, in: New Advances in Transcendence Theory, Proc. conf. Durham 1986, , ed., Cambridge University Press, pp. 229–247.
(1985), Conjecture in “Open Problems” section, in: Proc. Symposium on Analytic Number Theory, London, 25.Google Scholar
(2004),Mixing and linear equations over groups in positive characteristic, Israel J. Math. 142, 189–204.CrossRefGoogle Scholar
and (1983), Fields of large transcendence degree generated by values of elliptic functions, Invent. Math. 72, 407–464.CrossRefGoogle Scholar
(2000), An explicit lower bound for a homogeneous rational linear form in logarithms of algebraic numbers, II. Izvestiya: Mathematics 64, 1217–1269.Google Scholar
(1995), Division points on semi-abelian varieties, Invent. Math. 120 (1995), 143–159.CrossRefGoogle Scholar
(1981), Corps euclidiens, unités exceptionnelles et courbes elliptiques, J. Number Theory 13, 123–137.CrossRefGoogle Scholar
(1910), Geometrie der Zahlen, Teubner (Posthumously published; prepared by D. Hilbert and A. Speiser).
and (2002), The Mordell-Lang conjecture in positive characteristic revisited, In: Model theory and applications, Quaderni di matematica 11, L. Belair, , , , , and , eds. Dipartimento di Matematica Seconda Universit`a di Napoli. pp. 273–296.Google Scholar
and (2004), F-structures and integral points on semiabelian varieties over finite fields, Amer. J. Math. 126, 473–522.Google Scholar
(1922a), On the rational solutions of the indeterminate equations of the third and fourth degrees, Proc. Cambridge Philos. Soc. 21, 179–192.Google Scholar
(1922b), Note on the integer solutions of the equation Ey2 = Ax3 + Bx2 + Cx + D, Messenger Math. 51, 169–171.Google Scholar
(1923), On the integer solutions of the equation ey2 = ax3 + bx2 + cx + d, Proc. London Math. Soc. (2) 21, 415–419.Google Scholar
and (1990), Some Ramanujan-Nagell equations with many solutions, Indag Math. (N. S.), 1, 465–472.CrossRefGoogle Scholar
and (1994), Rational periodic points of rational functions, Intern. Math. Res. Not. (2), 97–110.Google Scholar
(2000), S-unit equations in function fields via the abc-theorem, Bull. London Math. Soc. 32, 163–170.CrossRefGoogle Scholar
and (2013), Modular forms and effective Diophantine approximation, J. Number Theory 133, 3739–3754.CrossRefGoogle Scholar
(1964), Sur une propriété des unités d'un corps algébrique, Arkiv för Mat. 5, 343–356.CrossRefGoogle Scholar
(1967), Sur les discriminants des nombres algébriques, Arkiv för Mat. 7, 265–282.CrossRefGoogle Scholar
(1968a), Quelques propriétés des nombres algébriques du quatri`eme degré, Arkiv för Mat. 7, 517–525.Google Scholar
(1968b), Sur les unités dans les corps biquadratiques primitifs du premier rang, Arkiv för Mat. 7, 359–394.CrossRefGoogle Scholar
(1970), Sur un type particulier d'unités algébriques, Arkiv för Mat. 8, 163– 184.CrossRefGoogle Scholar
(1989), Polynomial cycles in algebraic number fields, Colloq. Math. 58, 149–153.CrossRefGoogle Scholar
and (1997), Finite Polynomial Orbits in Finitely Generated Domains, Monatsh. Math. 124, 309–316.CrossRefGoogle Scholar
(1992), Algebraische Zahlentheorie, Springer Verlag.
(1986), Proof of Masser's Conjecture on the Algebraic Independence of Values of Liouville Series, Proc. Japan Acad. Ser. A 62, 219–222.Google Scholar
(1987), Conditions for algebraic independence of certain power series of algebraic numbers, Compos. Math. 62, 53–61.Google Scholar
(1994), Algebraic independence by Mahler'smethod and S-unit equations, Compos. Math. 92, 87–110.Google Scholar
(1996), Mahler Functions and Transcendence, Lecture Notes Math. 1631, Springer Verlag.
(1950), The p-adic generalization of the Thue-Siegel theorem, Acta Math. 83, 1–100.CrossRefGoogle Scholar
(2014), Arithmetic problems around the abc-conjecture and connections with logic, Ph.D. thesis, Queen's University, Canada.
and (1986), Products of prime powers in binary recurrence sequences I. The hyperbolic case, with an application to the generalized Ramanujan-Nagell equation, Math. Comp. 47, 713–727.Google Scholar
(2014), An algorithm determining cycles of polynomial mappings in integral domains, Publ. Math. Debrecen 84, 399–414.CrossRefGoogle Scholar
(1997), On distribution of solutions of S-unit equations, J. Number Theory 62, 221–241.CrossRefGoogle Scholar
and (1982), The growth condition for recurrence sequences, Macquarie University Math. Rep. 82–0041.Google Scholar
and (1991), Additive relations in fields, J. Austral. Math. Soc. (Ser. A) 51, 154–170.CrossRefGoogle Scholar
and (1965), Polynomials that divide infinitely many trinomials, Michigan Math. J., 12, 339–348.Google Scholar
(2000a), Inégalité de Vojta en dimension supérieure, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 29, 101–151.Google Scholar
(2003), Approximation diophantienne sur les variétés semi-abeliennes, Ann. Sci. Ecole Norm. Sup. (4) 36, 191–212.Google Scholar
(1958), The p-adic generalization of the Thue-Siegel-Roth Theorem, Mathematika 5, 40–48.CrossRefGoogle Scholar
, and (2014), A refinement of the abc conjecture, Bull. London Math. Soc. 46, 1156–1166.Google Scholar
(1957), Einheiten und Divisorenklassen in endlich erzeugbaren Körpern, Jahresber. Deutsch. Math. Verein 60, 1–21.Google Scholar
and (1962), Approximate formulas for some functions of prime numbers, Illinois J. Math. 6, 64–94.Google Scholar
and (1997), Schmidt's subspace theorem with moving targets, Invent. Math. 127, 51–65.CrossRefGoogle Scholar
and (1991), Integral points of Pn \ {2n + 1 hyperplanes in general position}, Invent. Math. 106, 195–216.CrossRefGoogle Scholar
(1976a), Linearformen mit algebraischen Koeffizienten, Manuscripta Math. 18, 147–185.CrossRefGoogle Scholar
(1976b), Die p-adische Verallgemeinerung des Satzes von Thue- Siegel-Roth-Schmidt,J. Reine Angew. Math. 288, 86–105.Google Scholar
(1976c), On products of special linear forms with algebraic coefficients,Acta Arith. 31, 389–398.CrossRefGoogle Scholar
(1977a), Über die diophantische Gleichung x1 +· · ·+xn = 0, Acta Arith. 33 (1977), 183–185.Google Scholar
(1977b), The p-adic Thue-Siegel-Roth-Schmidt theorem, Arch. Math. (Basel) 29, 267–270.CrossRefGoogle Scholar
(1977d), On linear forms with algebraic coefficients and Diophantine equations, J. Number Theory 9, 381–392.CrossRefGoogle Scholar
(1992), The quantitative Subspace Theorem for number fields, Compos. Math. 82, 245–273.Google Scholar
and (2000), The Number of Solutions of Polynomial- Exponential Equations, Compos. Math. 120, 193–225.CrossRefGoogle Scholar
and (1999), Polynomials that divide many k-nomials, in: Number Theory in Progress, Vol. I, Proc. conf. in honour of the 60th birthday of Andrzej Schinzel, , and eds. de Gruyter, pp. 445–450.Google Scholar
and (1997), Lower bounds for the heights of solutions of linear equations, Invent. Math. 129, 1–10.CrossRefGoogle Scholar
(1971), Linearformen mit algebraischen Koeffizienten II, Math. Ann. 191, 1–20.CrossRefGoogle Scholar
(1973), Inequalities for resultants and for decomposable forms, in: Diophantine Approximation and its Applications, Academic Press, pp. 235– 253.
(1975), Simultaneous approximation to algebraic numbers by elements of a number field, Monatsh. Math. 79, 55–66.CrossRefGoogle Scholar
(1978), Thue's equation over function fields, J. Austral. Math. Soc. Ser A 25, 385–422.CrossRefGoogle Scholar
(1990), The number of solutions of norm form equations, Trans. Amer. Math. Soc. 317, 197–227.CrossRefGoogle Scholar
(1991), Diophantine Approximations and Diophantine Equations, Lecture Notes Math. 1467, Springer Verlag.Google Scholar
(1996), Heights of points on subvarieties of Gnm, In: Number Theory 1993–94, London Math. Soc. Lecture Note Ser. 235, , ed., 157–187. Cambridge University Press.Google Scholar
(1999), The zero multiplicity of linear recurrence sequences, Acta Math. 182, 243–282.CrossRefGoogle Scholar
(2003), Linear recurrence sequences, in: Diophantine Approximation, C.I.M.E. Summer school, Cetraro, Italy, June 28–July 6, 2000, , , eds., Lecture Notes Math. 1819, Springer Verlag, pp. 171–247.Google Scholar
(2009), The Diophantine equation ax11· · · axnn = f (x1, . . ., xn), in: Analytic Number Theory. Essays in Honour of Klaus Roth,,, and , eds., pp. 414–420. Cambridge University Press.Google Scholar
(1934), Transzendenzuntersuchungen periodischer Funktionen: I Transzendenz von Potenzen; II Transzendenzeigenschaften elliptischer Funktionen, J. Reine Angew. Math. 172, 65–74.Google Scholar
(1978), Topics in Group Rings, Marcel Dekker.
(1926), The integer solutions of the equation y2 = axn|+ bxn-1 +· · ·+k, J. London Math. Soc. 1, 66–68.Google Scholar
(1929), Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss., Phys. Math. Kl., No. 1.Google Scholar
(1984), The S-unit equation over function fields, Math. Proc. Camb. Phil. Soc. 95, 3–4.CrossRefGoogle Scholar
(1995), Exceptional units and numbers of small Mahler measure, Experiment. Math. 4, 70–83.CrossRefGoogle Scholar
(1970), The solution of a decision problem for several classes of rings, Pacific J. Math. 34, 547–557.CrossRefGoogle Scholar
(1933), Einige Sätzeüber gewisse Reihenentwicklungen und exponentiale Beziehungen mit Anwendung auf diophantische Gleichungen, Oslo Vid. akad. Skrifter 6, 1–61.Google Scholar
(1935), EinVerfahren zur Behandlung gewisser exponentialer Gleichungen, 8. Skand. Mat.-Kongr. Stockholm163–188.Google Scholar
(1995), The solution of triangularly connected decomposable form equations, Math. Comp. 64, 819–840.CrossRefGoogle Scholar
(1997), S-unit equations, binary forms and curves of genus 2, Proc. London Math. Soc. (3) 75, 271–307.Google Scholar
(1998), The Algorithmic Resolution of Diophantine Equations, Cambridge University Press.CrossRefGoogle Scholar
(1999), Determining the small solutions to S-unit equations, Math. Comput. 68, 1687–1699.CrossRefGoogle Scholar
(1969), Effective estimates in “ternary” exponential diophantine equations (Russian), Dokl. Akad. Nauk BSSR, 13, 777–780.Google Scholar
(1973), Squarefree divisors of polynomials and class numbers of algebraic number fields (Russian), Acta Arith. 24, 143–149.Google Scholar
(1974), Representation of numbers by the norm forms with two dominating variables, J. Number Theory, 6, 481–486.CrossRefGoogle Scholar
(1976), A hyperelliptic diophantine equation and class numbers (Russian), Acta Arith. 30, 95–108.Google Scholar
(1981), Polynomial identities and Hauptmodulen, Quart. J. Math. Oxford Ser. (2) 32, 349–370.CrossRefGoogle Scholar
and (1994), Solving elliptic Diophantine equations by estimating linear forms in elliptic logarithms, Acta Arith. 67, 177–196.CrossRefGoogle Scholar
(1973), Class numbers of totally imaginary quadratic extensions of totally real fields, Trans. Amer. Math. Soc. 175, 209–232.CrossRefGoogle Scholar
(2007), Sur léffectivité du théor`e me de Siegel et la conjecture abc, J. Number Theory, 124, 267-290.CrossRefGoogle Scholar
(1975), On sets of integers containing no k elements in arithmetic progression, Acta Arith. 27, 299–345.CrossRefGoogle Scholar
and (1995), Ring-theoretic properties of certain Hecke algebras, Ann. Math. (2) 141, 553–572.Google Scholar
(1998), A space efficient algorithm for group structure computation, Math. Comp. 67, 1637–1663.CrossRefGoogle Scholar
(1909), Über Annäherungswerte algebraischer Zahlen, J. Reine Angew. Math. 135, 284–305.Google Scholar
(2005), Asymptotic estimates for the number of integer solutions to decomposable form inequalities, Compos. Math. 141 (2005), 271–292.CrossRefGoogle Scholar
and (2007), Units generating the ring of integers of complex cubic fields, Colloq. Math. 109, 71–83.CrossRefGoogle Scholar
(2013), Elliptic Diophantine Equations, de Gruyter.
and (1989), On the practical solution of the Thue equation, J. Number Theory 31, 99–132.CrossRefGoogle Scholar
(2014), Heights on groups and small multiplicative dependencies, Trans. Amer. Math. Soc. 366, 3295–3323.Google Scholar
(1983), Integral points on varieties, Ph.D.-thesis, Harvard University.
(1987), Diophantine Approximation and Value Distribution Theory, Lecture Notes in Math. 1239. Springer Verlag.CrossRefGoogle Scholar
(1996), Integral points on subvarieties of semiabelian varieties, I, Invent Math. 126, 133–181.CrossRefGoogle Scholar
(2000), On the ABC-conjecture and diophantine approxination by rational points, Amer. J. Math. 122, 843–872. Correction, Amer. J. Math. 123 (2001), 383–384.CrossRefGoogle Scholar
(1985), Diagonal equations over function fields, Bol. Soc. Bras. Mat. 16, 29–39.CrossRefGoogle Scholar
(1998), The equation ax + by = 1 in characteristic p, J. Number Th. 73, 195–200.CrossRefGoogle Scholar
(1996), An effective lower bound for the height of algebraic numbers, Acta Arith. 74, 81–95.CrossRefGoogle Scholar
(2014), Modules with many non-associates and norm form equations with many families of solutions, J. Number Theory 138, 20–36.CrossRefGoogle Scholar
(1973), Propriétés arithmétiques des valeurs de fonctions méromorphes algébriquement indépendantes, Acta Arith. 23, 19–88.CrossRefGoogle Scholar
(1974), Nombres Transcendants, Springer Verlag.
(2000), Diophantine approximation on linear algebraic groups, Springer Verlag.CrossRefGoogle Scholar
(1996), The truncated second main theorem of function fields, J. Number Theory 58, 139–157.CrossRefGoogle Scholar
(1999), A note onWronskians and the ABC theorem, Manuscripta Math. 98, 255–264.CrossRefGoogle Scholar
(1987), Algorithms for Diophantine Equations, Dissertation, Centrum voor Wiskunde en Informatica, Amsterdam.Google Scholar
(1997), Über das Lösen von Einheiten- und Indexformgleichungen in algebraischen Zahlkörpern mit einer Anwerdung auf die Bestimmung aller ganzen Punkte einer Mordellschen Kurve, Dissertation, Technical University, Berlin.
(2000), Über das Lösen von Einheiten- und Indexformgleichungen in algebraischen Zahlkörpern, J. Number Theory 82, 188–224.CrossRefGoogle Scholar
(1995), Modular elliptic curves and Fermat's Last Theorem, Ann. Math. (2) 141, 443–551.CrossRefGoogle Scholar
(1971), On approximation of algebraic numbers by algebraic numbers of bounded degree, in: Proc. Sympos. Pure Math. 20, Amer. Math. Soc., Providence, pp. 213–247.Google Scholar
, ed. (2002), A panorama of number theory or the view from Baker's garden, Cambridge University Press.CrossRefGoogle Scholar
(2007), P-adic logarithmic forms and group varieties III, Forum Mathematicum, 19, 187–280.CrossRefGoogle Scholar
(1993), Some remarks on the S-unit equation in function fields, Acta Arith. 64, 87–98.CrossRefGoogle Scholar
(2003), Some applications of diophantine approximation to diophantine equations (with special emphasis on the Schmidt subspace theorem), Forum.Google Scholar
(2004), On the integer solutions of exponential equations in function fields, Ann. Inst. Fourier (Grenoble) 54, 849–874.Google Scholar
(2009), Lecture notes on Diophantine analysis, Edizioni della Normale.
(2012), Some Problems of Unlikely Intersections in Arithmetic and Geometry, Princeton University Press.
(1996), Cycles of polynomial mappings, Ph.D. thesis, University of California, Berkeley.