Généralisation du critère de Beurling et Nyman pour l'hypothèse de Riemann

We generalise the Beurling-Nyman criterion, already known for the Riemann ζ function, to a larger class of Dirichlet series. We link the density of some subspace of functions in L2(0,1) and the localization of the zeros of a Dirichlet series. To do so, we use the structure of the Hardy space of the half-plane. To cite this article: A. de Roton, C. R. Acad. Sci. Paris, Ser. I 340 (2005).