Généralisation du critère de Beurling-Nyman pour l'hypothèse de Riemann.

Anne de Roton (1)

1 IECN - Institut Élie Cartan de Nancy

We generalise Beurling-Nyman's criterion, already known for the Riemann zeta function, to a larger class of Dirichlet series. We reveal a link between the density of some subspace of functions in L^2(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.

Mots clés: Hardy spaces; Dirichlet series; Beurling-Nyman criterion; generalised Riemann hypothesis; Selberg class; Hardy spaces.

Domaines: Théorie des nombres [math.NT]

Anne de Roton. Généralisation du critère de Beurling-Nyman pour l'hypothèse de Riemann.. Transactions of the American Mathematical Society, 2007, 359, pp.6079-6110. ⟨10.1090/S0002-9947-07-04261-4⟩. ⟨hal-00091952⟩