Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-01104234v1

Volume: Volume 6

Published on: January 1, 1983

Submitted on: March 3, 2015

Keywords: continued fraction,Riemann zeta function,Gabriel's theorem,[MATH] Mathematics [math]

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