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 publicationAIP Conference Proceedings
Pages116-123
Number of pages8
Volume1385
DOIs
Publication statusPublished - 2011
EventDiophantine Analysis and Related Fields 2011, DARF - 2011 - Musashino, Tokyo, Japan
Duration: 2011 Mar 32011 Mar 5

Other

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

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products
expansion

Keywords

  • Algebraic independence
  • infinite products
  • Mahler's method

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Algebraic independence properties related to certain infinite products. / Tanaka, Takaaki.

AIP Conference Proceedings. Vol. 1385 2011. p. 116-123.

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

Tanaka, T 2011, Algebraic independence properties related to certain infinite products. in AIP Conference Proceedings. vol. 1385, pp. 116-123, Diophantine Analysis and Related Fields 2011, DARF - 2011, Musashino, Tokyo, Japan, 11/3/3. https://doi.org/10.1063/1.3630047
Tanaka, Takaaki. / Algebraic independence properties related to certain infinite products. AIP Conference Proceedings. Vol. 1385 2011. pp. 116-123
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