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

hrj:96 - Hardy-Ramanujan Journal, January 1, 1983, Volume 6 - 1983 - https://doi.org/10.46298/hrj.1983.96
Mean-value of the Riemann zeta-function and other remarks III

Authors: K Ramachandra

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.

Volume: Volume 6 - 1983
Published on: January 1, 1983
Imported on: March 3, 2015
Keywords: continued fraction,Riemann zeta function,Gabriel's theorem,[MATH] Mathematics [math]