Algebraic independence results for the sixteen families of \(q\)-series

DOI10.1007/s11139-010-9235-4zbMath1256.11040OpenAlexW2076254431MaRDI QIDQ993488

Yohei Tachiya, Carsten Elsner, Iekata Shiokawa, Shun Shimomura

Publication date: 20 September 2010

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-010-9235-4

zbMATH Keywords

\(q\)-seriesJacobian elliptic functionsalgebraic independenceNesterenko's theoremRamanujan functions

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Transcendence (general theory) (11J81)

Related Items (1)

Algebraic independence of certain numbers related to modular functions

Cites Work

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• Linear independence of values of a certain Lambert series
• Sixteen Eisenstein series
• Algebraic relations for reciprocal sums of even terms in Fibonacci numbers
• Algebraic relations for reciprocal sums of odd terms in Fibonacci numbers
• A remark on Nesterenko's theorem for Ramanujan functions
• The Summation of Series of Hyperbolic Functions
• Modular functions and transcendence questions
• Algebraic relations for reciprocal sums of Fibonacci numbers
• Introduction to algebraic independence theory. With contributions from F. Amoroso, D. Bertrand, W. D. Brownawell, G. Diaz, M. Laurent, Yu. V. Nesterenko, K. Nishioka, P. Philippon, G. Rémond, D. Roy, M. Waldschmidt

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