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 |
|---|---|
| Pages (from-to) | 939-948 |
| Number of pages | 10 |
| Journal | Illinois Journal of Mathematics |
| Volume | 45 |
| Issue number | 3 |
| Publication status | Published - 2001 Sep |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Differential transcendence of a class of generalized Dirichlet series
AU - Amou, Masaaki
AU - Katsurada, Masanori
PY - 2001/9
Y1 - 2001/9
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.
UR - http://www.scopus.com/inward/record.url?scp=0039248474&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0039248474&partnerID=8YFLogxK
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 -