Algebraic independence of certain numbers related to modular functions

DOI10.7169/facm/2012.47.1.10zbMath1290.11109OpenAlexW2086185819MaRDI QIDQ714399

Carsten Elsner, Iekata Shiokawa, Shun Shimomura

Publication date: 21 October 2012

Published in: Functiones et Approximatio. Commentarii Mathematici (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.facm/1348578282

zbMATH Keywords

gamma functioncomplete elliptic integralsalgebraic independenceNesterenko's theoremRamanujan functions

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Algebraic independence; Gel'fond's method (11J85) Transcendence theory of other special functions (11J91) Transcendence theory of elliptic and abelian functions (11J89)

Related Items (1)

On algebraic relations for Ramanujan's functions

Cites Work

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• On Ramanujan's function \(k(q)=r(q)r^{2}(q^{2})\)
• Algebraic independence results for the sixteen families of \(q\)-series
• Transcendence of the log gamma function and some discrete periods
• Quintic and septic Eisenstein series
• Sixteen Eisenstein series
• Two remarks on transcendental numbers
• A remark on Nesterenko's theorem for Ramanujan functions
• Algebraic independence results for reciprocal sums of Fibonacci numbers
• Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind
• The Summation of Series of Hyperbolic Functions
• Modular functions and transcendence questions
• Algebraic relations for reciprocal sums of Fibonacci numbers
• Ramanujan's Lost Notebook
• On Epstein's Zeta-function.

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