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Results in Mathematics

, Volume 48, Issue 3–4, pp 344–370 | Cite as

Transcendence of the values of infinite products in several variables

  • Yohei TachiyaEmail author
Article

Abstract

The aim of this paper is to prove the transcendence of certain infinite products. As applications, we get necessary and sufficient conditions for transcendence of the value of \(\Pi_{k=0}^{\infty}(1+a_{k}^{(1)}{z_{1}r^{k}}+\cdot\cdot\cdot+a_{k}^{(m)}{z_{m}r^{k}})\) at appropriate algebraic points, where r ≥ 2 is an integer and {an (i)}n≥ 0 (1 ≤ im) are suitable sequences of algebraic numbers.

Mathematics Subject Classification (2000)

11J81 

Keywords

Infinite products Transcendence Mahler’s method 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of MathematicsKeio UniversityYokohamaJapan

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