Differential transcendence of a class of generalized Dirichlet series

Masaaki Amou; Masanori Katsurada

doi:10.1215/ijm/1258138161

Differential transcendence of a class of generalized Dirichlet series

Masaaki Amou, Masanori Katsurada

Research output: Contribution to journal › Article › peer-review

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Abstract

We investigate differential transcendence properties for a generalized Dirichlet series of the form ∑^∞_n=0 a_nλ^-s_n. 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 language	English
Pages (from-to)	939-948
Number of pages	10
Journal	Illinois Journal of Mathematics
Volume	45
Issue number	3
DOIs	https://doi.org/10.1215/ijm/1258138161
Publication status	Published - 2001
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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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.",

author = "Masaaki Amou and Masanori Katsurada",

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AB - 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.

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DO - 10.1215/ijm/1258138161

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Differential transcendence of a class of generalized Dirichlet series

Abstract

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