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 language | English |
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Pages (from-to) | 939-948 |
Number of pages | 10 |
Journal | Illinois Journal of Mathematics |
Volume | 45 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2001 |
Externally published | Yes |
ASJC Scopus subject areas
- Mathematics(all)