Zero free regions for Dirichlet series
  In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for $L$-functions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Roton. As a concrete application, we get, for example, a Beurling-Nyman type criterion for the Siegel zero problem. 
Christophe Delaunay (ICJ), Emmanuel Fricain (ICJ), Elie Mosaki (ICJ),   Olivier Robert
math.NT math.FA