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

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

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