Proof of some conjectures on the mean-value of Titchmarsh series-II

Abstract

International audience In this paper, we give lower bounds for $\int_0^H \vert F(it)\vert^k\,dt$, where $k=1$ or $2$ and $F(s)$ is a Dirichlet series of a certain kind. Since the conditions on $F(s)$ are relaxed, the bounds are somewhat smaller than those obtained previously.