## R Balasubramanian ; K Ramachandra - Proof of some conjectures on the mean-value of Titchmarsh series I.

hrj:118 - Hardy-Ramanujan Journal, January 1, 1990, Volume 13 - https://doi.org/10.46298/hrj.1990.118
Proof of some conjectures on the mean-value of Titchmarsh series I.

Authors: R Balasubramanian ; K Ramachandra

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 $\int_0^H \vert F(it)\vert^k\,dt$, where $k=1$ or $2$. In this paper, better results and a proof of the conjecture are obtained.

Volume: Volume 13
Published on: January 1, 1990
Submitted on: March 3, 2015
Keywords: mean-value.,Titchmarsh series,[MATH] Mathematics [math]