Zero-free regions for Dirichlet series (II)

Emmanuel Fricain (1) , Christophe Delaunay (2) , Elie Mosaki (1) , Olivier Robert (3)

1 ICJ - Institut Camille Jordan
2 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
3 LA MUSE - Laboratoire de Mathématiques Unifiées de Saint-Etienne

In this paper, we continue some work devoted to explicit zero-free discs for a large class of Dirichlet series. In a previous article, such zero-free regions were described using some spaces of functions which were defined with some technical conditions. Here we give two different natural ways in order to remove those technical conditions. In particular this allows to right down explicit zero-free regions differently and to obtain for them an easier description useful for direct applications.

Mots clés: Pascal matrix; Dirichlet series; Beurling--Nyman criterion; Hardy spaces; zeros of $L$-functions; Pascal matrix.

Domaines: Analyse fonctionnelle [math.FA]; Théorie des nombres [math.NT]

Emmanuel Fricain, Christophe Delaunay, Elie Mosaki, Olivier Robert. Zero-free regions for Dirichlet series (II). Mathematische Zeitschrift, 2013, 273 (3-4), pp.999-1023. ⟨hal-00647041⟩