Essential singularities of Euler products

Gautami Bhowmik (1) , Jan-Christoph Schlage-Puchta (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 Mathematisches institut

We classify singularities of Dirichlet series having Euler products which are rational functions for p and p^{-s} for p a prime number and give examples of natural boundaries from zeta functions of groups and height zeta functions.

Mots clés: Dirichlet series; Euler product; singularities; natural boundary; zeta functions of groups

Domaines: Théorie des nombres [math.NT]

Gautami Bhowmik, Jan-Christoph Schlage-Puchta. Essential singularities of Euler products. 2009. ⟨hal-00446359⟩