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Generalisation of Beurling-Nyman's criterion for Riemann hy- pothesis) We generalise Beurling-Nyman's criterion, already known for the Riemannfunc- tion, to a larger class of Dirichlet series. We reveal a link between 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-plan.

Généralisation du critère de Beurling-Nyman pour l’hypothèse de Riemann