Mean-value of the Riemann zeta-function and other remarks III

K Ramachandra (1)

1 TIFR - Tata Institute for Fundamental Research

The results given in these papers continue the theme developed in part I of this series. In Part III we prove $M(\frac{1}{2})>\!\!\!>_k (\log H_0/q_n)^{k^2}$, where $p_m/q_m$ is the $m$th convergent of the continued fraction expansion of $k$, and $n$ is the unique integer such that $q_nq_{n+1}\geq \log\log H_0 > q_nq_{n-1}$. Section 4 of part III discusses lower bounds of mean values of Titchmarsh series.

Mots clés: Gabriel's theorem; Riemann zeta function; continued fraction

Domaines: Mathématiques [math]

K Ramachandra. Mean-value of the Riemann zeta-function and other remarks III. Hardy-Ramanujan Journal, 1983, Volume 6 - 1983, pp.1-21. ⟨10.46298/hrj.1983.96⟩. ⟨hal-01104234⟩