Le critère de Li et lʹhypothèse de Riemann pour la classe de Selberg Original Research Article

We generalise Liʹs criterion, already known for the Riemann zeta function, to a large class of Dirichlet series. We give first an explicit formula for the coefficients image, for all positive integers n and ρ runs over all the non-trivial zeros of a function F in this class. To do so, we use the Weil Explicit Formula.