APÉRY LIMITS FOR ELLIPTIC -VALUES

DOI10.1017/S0004972721001295zbMath1503.11082arXiv2111.08796OpenAlexW4206048007MaRDI QIDQ5867865

Christoph Koutschan, Wadim Zudilin

Publication date: 19 September 2022

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.08796

zbMATH Keywords

Mahler measurerecurrence equationcreative telescopingBeukers integralApéry limit

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Continued fractions and generalizations (11J70) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) PV-numbers and generalizations; other special algebraic numbers; Mahler measure (11R06) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Linear difference equations (39A06)

Related Items (1)

Diophantine approximations. Abstracts from the workshop held April 17--23, 2022

Uses Software

• HolonomicFunctions
• MultiZeilberger
• DEtools

Cites Work

• The method of differentiating under the integral sign
• Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory
• A fast algorithm for proving terminating hypergeometric identities
• A proof that Euler missed. Apéry's proof of the irrationality of \(\zeta(3)\). An informal report
• Linear independence of dilogarithmic values
• Tweaking the Beukers integrals in search of more miraculous irrationality proofs a la Apéry
• A Note on the Irrationality of ζ(2) and ζ(3)
• Apéry Limits: Experiments and Proofs
• Many Variations of Mahler Measures
• Regulator of modular units and Mahler measures
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