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

Takeshi Kurosawa, Yohei Tachiya, Takaaki 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 language English 77-104 28 Monatshefte fur Mathematik 174 1 https://doi.org/10.1007/s00605-014-0617-3 Published - 2014

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Independence Results
Algebraic Independence
Infinite product
Linear Recurrence
Entire Function
Zero
Subsequence
Functional equation
Multiplicative
Derivative

### Keywords

• Algebraic independence
• Infinite products
• Mahler functions

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

Algebraic independence results for the values of certain Mahler functions and their application to infinite products. / Kurosawa, Takeshi; Tachiya, Yohei; Tanaka, Takaaki.

In: Monatshefte fur Mathematik, Vol. 174, No. 1, 2014, p. 77-104.

Research output: Contribution to journalArticle

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