An extremal problem related to generalizations of the Nyman-Beurling and Báez-Duarte criteria

Abstract

We establish generalizations of the Nyman-Beurling and Báez-Duarte criteria concerning lack of zeros of Dirichlet $L$-functions in the semi-plane $\Re (s)>1/p$ for $p\in (1,2]$. We pose and solve a natural extremal problem for Dirichlet polynomials which take values one at the zeros of the corresponding $L$-function on the vertical line $\Re (s)=1/p$.