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K. F. Roth

doi:10.1112/S0025579300000826

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On page 2 of my paper “Rational approximations to algebraic numbers” [Mathematika 2 (1955), 1–20], I referred to possible generalizations of my theorem, and mentioned that I had proved the following:

Let α be any algebraic number, not rational. If the inequality

is satisfied by infinitely many algebraic numbers β of degree g, then κ ≤ 2g.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Richtmyer, R. D. Devaney, Marjorie and Metropolis, N. 1962. Continued fraction expansions of algebraic numbers. Numerische Mathematik, Vol. 4, Issue. 1, p. 68.

Lew, John S. and Rosenberg, Arnold L. 1978. Polynomial indexing of integer lattice-points II. Nonexistence results for higher-degree polynomials. Journal of Number Theory, Vol. 10, Issue. 2, p. 215.

Nettler, Gideon 1981. Transcendental continued fractions. Journal of Number Theory, Vol. 13, Issue. 4, p. 456.

Luckhardt, H. 1989. Herbrand-Analysen zweier Beweise des Satzes von Roth: Polynomiale Anzahlschranken. Journal of Symbolic Logic, Vol. 54, Issue. 1, p. 234.

Bullett, Shaun and Sentenac, Pierrette 1994. Ordered orbits of the shift, square roots, and the devil's staircase. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 115, Issue. 3, p. 451.

Mclaughlin, Joyce R. 1995. Proceedings of the International Congress of Mathematicians. p. 1494.

Banks, William D. and Shparlinski, Igor E. 2006. Non-residues and primitive roots in Beatty sequences. Bulletin of the Australian Mathematical Society, Vol. 73, Issue. 3, p. 433.

Monks, Keenan Peluse, Sarah and Ye, Lynnelle 2013. Strings of special primes in arithmetic progressions. Archiv der Mathematik, Vol. 101, Issue. 3, p. 219.

Horner, Jennifer Modayil, Maria Chapman, Laura Roche and Dinh, An 2016. Consent, Refusal, and Waivers in Patient-Centered Dysphagia Care: Using Law, Ethics, and Evidence to Guide Clinical Practice. American Journal of Speech-Language Pathology, Vol. 25, Issue. 4, p. 453.

Chen, Huei-Jeng 2018. Baker–Schmidt theorem for Hausdorff dimensions in finite characteristic. Finite Fields and Their Applications, Vol. 52, Issue. , p. 336.

Banks, William D. and Guo, Victor Z. 2018. Consecutive primes and Beatty sequences. Journal of Number Theory, Vol. 191, Issue. , p. 158.

Wananiyakul, Saeree Laohakosol, Vichian and Tongsomporn, Janyarak 2022. Mathematical, Computational Intelligence and Engineering Approaches for Tourism, Agriculture and Healthcare. Vol. 214, Issue. , p. 111.

Guo, Victor Zhenyu Li, Jinjiang and Zhang, Min 2022. Piatetski-Shapiro primes in the intersection of multiple Beatty sequences. Rocky Mountain Journal of Mathematics, Vol. 52, Issue. 4,

ÇAM ÇELİK, Şermin 2022. k-Free numbers and integer parts of αp. Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, Vol. 71, Issue. 1, p. 237.

Akbal, Yıldırım and Güloğlu, Ahmet M. 2023. Variations on a theme of Mirsky. International Journal of Number Theory, Vol. 19, Issue. 01, p. 1.

Guo, Victor Zhenyu Li, Jinjiang and Zhang, Min 2023. Beatty primes from fractional powers of almost-primes. Indagationes Mathematicae, Vol. 34, Issue. 6, p. 1254.

Banks, William and Shparlinski, Igor E. 2024. On the Greatest Common Divisor of Integer Parts of Polynomials. Michigan Mathematical Journal, Vol. -1, Issue. -1,

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