Differential transcendence of a class of generalized Dirichlet series

Masaaki Amou, Masanori Katsurada

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We investigate differential transcendence properties for a generalized Dirichlet series of the form ∑n=0 anλ-sn. Our treatment of this series is purely algebraic and does not rely on any analytic properties of generalized Dirichlet series. We establish differential transcendence theorems for a certain class of generalized Dirichlet series. These results imply that the Hurwits zeta-function ζ(s, a) does not satisfy an algebraic differential equation with complex coefficients.

Original languageEnglish
Pages (from-to)939-948
Number of pages10
JournalIllinois Journal of Mathematics
Volume45
Issue number3
Publication statusPublished - 2001 Sep
Externally publishedYes

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Transcendence
Dirichlet Series
Algebraic Differential Equations
Riemann zeta function
Imply
Series
Coefficient
Theorem
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Differential transcendence of a class of generalized Dirichlet series. / Amou, Masaaki; Katsurada, Masanori.

In: Illinois Journal of Mathematics, Vol. 45, No. 3, 09.2001, p. 939-948.

Research output: Contribution to journalArticle

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