A criterion of algebraic independence of values of modular functions and an application to infinite products involving Fibonacci and Lucas numbers

DOI10.1007/s40993-022-00328-7zbMath1493.11110OpenAlexW4229454649WikidataQ114218033 ScholiaQ114218033MaRDI QIDQ2145873

Yohei Tachiya, Masanobu Kaneko, Daniel Duverney, Carsten Elsner

Publication date: 15 June 2022

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40993-022-00328-7

zbMATH Keywords

modular functionsFibonacci numbersLucas numbersinfinite productsalgebraic independenceDedekind eta function

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Algebraic independence; Gel'fond's method (11J85) Dedekind eta function, Dedekind sums (11F20) Fibonacci and Lucas numbers and polynomials and generalizations (11B39)

Related Items (1)

Algebraic independence of values of quasi-modular forms

Cites Work

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• Theta functions and transcendence
• Transcendence of Jacobi's theta series
• A proof of the Mahler-Manin conjecture
• Algebraic independence of certain infinite products involving the Fibonacci numbers
• Intersection numbers of modular correspondences for genus zero modular curves
• Eta Products and Theta Series Identities
• Modular functions and transcendence questions

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