Algebraic independence results for the values of certain Mahler functions and their application to infinite products

Takeshi Kurosawa, Yohei Tachiya, Taka aki Tanaka

Research output: Contribution to journalArticle

Abstract

In this paper we establish algebraic independence criteria for the values at an algebraic point of Mahler functions each of which satisfies either a multiplicative type of functional equation or an additive one. As application we construct, using a linear recurrence sequence, an entire function defined by an infinite product such that its values as well as its all successive derivatives at algebraic points other than its zeroes are algebraically independent. Zeroes of such an entire function form a subsequence of the linear recurrence sequence. We prove the algebraic independency by reducing those values at algebraic points to those of Mahler functions.

Original languageEnglish
Pages (from-to)77-104
Number of pages28
JournalMonatshefte fur Mathematik
Volume174
Issue number1
DOIs
Publication statusPublished - 2014 May

Keywords

  • Algebraic independence
  • Infinite products
  • Mahler functions

ASJC Scopus subject areas

  • Mathematics(all)

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