502 research outputs found

    Open Diophantine Problems

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    We collect a number of open questions concerning Diophantine equations, Diophantine Approximation and transcendental numbers. Revised version: corrected typos and added references.Comment: 58 pages. to appear in the Moscow Mathematical Journal vo. 4 N.1 (2004) dedicated to Pierre Cartie

    Searching for Apery-Style Miracles [Using, Inter-Alia, the Amazing Almkvist-Zeilberger Algorithm]

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    Roger Apery's seminal method for proving irrationality is "turned on its head" and taught to computers, enabling a one second redux of the original proof of zeta(3), and many new irrationality proofs of many new constants, alas, none of them is both famous and not-yet-proved-irrational.Comment: 16 pages. Exclusively published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger, May 2014, and this arxiv.org. Accompanied my Maple package NesApery, available from http://www.math.rutgers.edu/~zeilberg/tokhniot/NesAper

    Thue's Fundamentaltheorem, I: The General Case

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    In this paper, Thue's Fundamentaltheorem is analysed. We show that it includes, and often strengthens, known effective irrationality measures obtained via the so-called hypergeometric method as well as showing that it can be applied to previously unconsidered families of algebraic numbers. Furthermore, we extend the method to also cover approximation by algebraic numbers in imaginary quadratic number fields.Comment: accepted version (Acta Arithmetica
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