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

R Balasubramanian (1) , K Ramachandra (1)

1 TIFR - Tata Institute for Fundamental Research

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.

Domaines: Mathématiques [math]

R Balasubramanian, K Ramachandra. Proof of some conjectures on the mean-value of Titchmarsh series-II. Hardy-Ramanujan Journal, 1991, Volume 14 - 1991, pp.1 - 20. ⟨10.46298/hrj.1991.121⟩. ⟨hal-01104764⟩