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On p-adic F-functions

Published online by Cambridge University Press:  09 April 2009

Wang Lianxiang
Wang Lianxiang
Affiliation:
School of Mathematics and PhysicsMacquarie UniversityNorth RydeNew South Wales 2113, Australia
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Abstract

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We introduce the class of p-adic F-functions which contains both the p-adic E-function and p-adic G-functions, as well as other functions. In this paper we obtain lower bounds for polynomials in the values at algebraic points of a class of p-adic F-functions defined over the completion of the algebraic closure of a p-adic field.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 35 , Issue 2 , October 1983 , pp. 269 - 280
Copyright
Copyright © Australian Mathematical Society 1983

References

Refernces

[1]Bachman, Georg, Introduction to p-adic numbers and valuation theory (Academic Press, New York).Google Scholar
[2]Bundschuh, Peter and Walliser, Rolf, ‘Untere Schranken für Polynome in Werten der p-adischen Exponentialfunktion’, Math. Ann. 244 (1979), 185–191.CrossRefGoogle Scholar
[3]Чиρcκиг, B. Λ [V. G. Čirskii], ‘Oб aρифmetичecκиx cβ⊙йctβax зиaчehий ahaлиtичecκиx фγhkций C aлγeбρaичecκиmи иρρaци⊙haлhβmи κoзффициehτamи ρядoβ Teйлoρa’ [Arithmetic properties of the values of analytic of analytic functions with algebraic irrtional coefficients of their taylor's series], Vestnik Moskov. Univ. Ser. I Mat. Meh. (3) 133 (1978), 29–34.Google Scholar
[4]Flicker, Y. Z., ‘On p-adic G-functions’, J. London Math. Soc. 15 (1977), 395–402.CrossRefGoogle Scholar
[5]Γaлoчκии, A. И. [A. I. Galochkin] лoчkhh ‘A. I. Galochkin’, ‘Oцehkи cиизγ mhoγoчлehob ot зhaчehий ahaлиtичeckиx фγhkций oдhoγo kлacca’ [Estimates from below of polynomials in the values of analytic functions of a certain class], Mat. Sb. 95 (137), 3 (11) (1974), 396–417.Google Scholar
[6]Hecrepehko, Ю. B. ‘Ju. V. Nesterenko’ ‘Oцeheи πoρядob Hγлeй фλhkций Oдhoto kлacca и иx зpилoxehия B Teopии tpahcцehдehthиx чhceд’ [Estimates for the orders of zeros of functions of a certain class and applications in the theory of transcendental numbers], Izu. Akad. Nauk SSSR Ser. Mat. (2) 41 (1977), 253–284.Google Scholar
[7]Ostrowski, A., ‘Sur les relations algébriques entre les integrales indefinies’, Acta Math. 78 (1946), 315–318.CrossRefGoogle Scholar
[8]Remmal, Salah-eddine, ‘Problèmes de transcedance lies aux E-fonctions et aux G-fonctions p-adiques’ Publications Mathématiques de I'Université Pierre et Marie Curié, Groupé d'´tude suv les problemes diophantiends, 1980/1981.Google Scholar
[9]Щидлobckий, A. Б. [A. B. Šidlovskũ], ‘O Tpahcцehдehthoctи и aлeбpaичeckoй Heзabиcиmocth зhaчeий цeлиx фλhkций Hekotopиx kлaccob’ [Transcdence and algebraic independence of the values of entire functions of certain classes] Moskov. Gos. Univ U^. Zup. 186 (1959), 11–70.Google Scholar
[10]Щиллobckий, A. Б., [A. B. Šidlovskũ], ‘O kpиtepии aлreбρaичeckoй heзaииcmpctи зhaчeиий oдhoto Kлacca цeлцx фλhkций’ [A criterion for algebraic independence of the values of a class of entire functions], Izu. Akad. Nauk SSSR Ser. Mat. 23 (1959), 35–66, Amer. Math. Soc. Transl. (2) 22 (1962), 339–370.Google Scholar
[11]Šidlovskil, A. B.‘On the estimates of the algebraic independence measures of the values of E-functions’, J. Austral. Math. Soc. Ser. A 27 (1979), 385–407.Google Scholar
[12]Siegel, C. L., ‘Über einige Anwendungen diophantischer Approximationen’, Abhandl. Preuss Akad. Wiss. Phys. Math. Kl (1929), No. 1, 1–70.Google Scholar
[13]Siegel, C. L., Transcendental numbers (Princeton University Press, 1949).Google Scholar
[14]Vaaler, J. D. and van der Poorten, A. J., ‘Bounds for solutions of systems of linear equations’, Bull. Austral. Math. Soc. 25 (1982), 125–132.CrossRefGoogle Scholar
[15]Waldschmidt, Michel, Nombres transcendants (Lecture Notes in Mathematics, 402, Springer-Verlag, Berlin, Heidelberg, New York, 1974).CrossRefGoogle Scholar