Differential transcendence of a class of generalized Dirichlet series
Amou, Masaaki ; Katsurada, Masanori
Illinois J. Math., Tome 45 (2001) no. 4, p. 939-948 / Harvested from Project Euclid
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We investigate differential transcendence properties for a generalized Dirichlet series of the form $\sum_{n=0}^\infty a_n\lambda_n^{-s}$. 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 $\zeta(s,a)$ does not satisfy an algebraic differential equation with complex coefficients.
Publié le : 2001-07-15
Classification:  11J91,  11M35,  11M41 
@article{1258138161,
     author = {Amou, Masaaki and Katsurada, Masanori},
     title = {Differential transcendence of a class of generalized Dirichlet series},
     journal = {Illinois J. Math.},
     volume = {45},
     number = {4},
     year = {2001},
     pages = { 939-948},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138161}
}

Amou, Masaaki; Katsurada, Masanori. Differential transcendence of a class of generalized Dirichlet series. Illinois J. Math., Tome 45 (2001) no. 4, pp.  939-948. http://gdmltest.u-ga.fr/item/1258138161/