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

Daniel Duverney, Carsten Elsner, Masanobu Kaneko, Yohei Tachiya

研究成果: ジャーナルへの寄稿学術誌査読

抄録

The aim of this paper is to give a criterion of algebraic independence for the values at the same point of two modular functions under certain conditions. As an application, we show that any two infinite products in ∏n=1∞(1+1Fn),∏n=3∞(1-1Fn),∏n=1∞(1+1Ln),∏n=2∞(1-1Ln)are algebraically independent over Q, where { Fn} and { Ln} are the Fibonacci and Lucas sequences, respectively. The proof of our main theorem is based on the properties of the field of all modular functions for the principal congruence subgroup, together with a deep result of Yu. V. Nesterenko on algebraic independence of the values of the Eisenstein series.

本文言語英語
論文番号31
ジャーナルResearch in Number Theory
8
2
DOI
出版ステータス出版済み - 6月 2022

!!!All Science Journal Classification (ASJC) codes

  • 代数と数論

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