Algebraic independence properties related to certain infinite products

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this paper we establish algebraic independence of the values of a certain infinite product as well as its all successive derivatives at algebraic points other than its zeroes, using the fact that the logarithmic derivative of an infinite product gives a partial fraction expansion. Such an infinite product is generated by a linear recurrence. The method used for proving the algebraic independence is based on the theory of Mahler functions of several variables.

Original languageEnglish
Title of host publicationDiophantine Analysis and Related Fields 2011, DARF - 2011
Pages116-123
Number of pages8
DOIs
Publication statusPublished - 2011 Nov 25
EventDiophantine Analysis and Related Fields 2011, DARF - 2011 - Musashino, Tokyo, Japan
Duration: 2011 Mar 32011 Mar 5

Publication series

NameAIP Conference Proceedings
Volume1385
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherDiophantine Analysis and Related Fields 2011, DARF - 2011
CountryJapan
CityMusashino, Tokyo
Period11/3/311/3/5

Keywords

  • Algebraic independence
  • Mahler's method
  • infinite products

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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  • Cite this

    Tanaka, T. A. (2011). Algebraic independence properties related to certain infinite products. In Diophantine Analysis and Related Fields 2011, DARF - 2011 (pp. 116-123). (AIP Conference Proceedings; Vol. 1385). https://doi.org/10.1063/1.3630047