TY - JOUR
T1 - Differential transcendence of a class of generalized Dirichlet series
AU - Amou, Masaaki
AU - Katsurada, Masanori
N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2001
Y1 - 2001
N2 - 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.
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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U2 - 10.1215/ijm/1258138161
DO - 10.1215/ijm/1258138161
M3 - Article
AN - SCOPUS:0039248474
VL - 45
SP - 939
EP - 948
JO - Illinois Journal of Mathematics
JF - Illinois Journal of Mathematics
SN - 0019-2082
IS - 3
ER -