Differential transcendence of a class of generalized Dirichlet series

Masaaki Amou, Masanori Katsurada

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1 Citation (Scopus)


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
Issue number3
Publication statusPublished - 2001
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics


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