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

R Balasubramanian (1) , K Ramachandra (1)

1 TIFR - Tata Institute for Fundamental Research

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.

Mots clés: Titchmarsh series; mean-value.

Domaines: Mathématiques [math]

R Balasubramanian, K Ramachandra. Proof of some conjectures on the mean-value of Titchmarsh series I.. Hardy-Ramanujan Journal, 1990, Volume 13 - 1990, pp.1 - 20. ⟨10.46298/hrj.1990.118⟩. ⟨hal-01104710⟩