Proof of some conjectures on the mean-value of Titchmarsh series I.

Let $F(s)$ be a Titchmarsh series, i.e. a kind of Dirichlet series, the coefficients of which are suitably bounded. This notion was introduced by us in an earlier paper where we stated a conjecture and proved certain theorems on the lower bound for ∫₀H F(it)ᵏ\,dt, where $k=1$ or $2$. In this paper, better results and a proof of the conjecture are obtained.