{"docId":96,"paperId":96,"url":"https:\/\/hrj.episciences.org\/96","doi":"10.46298\/hrj.1983.96","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":17,"name":"Volume 6 - 1983"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01104234","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01104234v1","dateSubmitted":"2015-03-03 16:13:37","dateAccepted":"2015-06-12 16:05:16","datePublished":"1983-01-01 08:00:00","titles":{"en":"Mean-value of the Riemann zeta-function and other remarks III"},"authors":["Ramachandra, K"],"abstracts":{"en":"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."},"keywords":[{"en":"continued fraction"},{"en":"Riemann zeta function"},{"en":"Gabriel's theorem"},"[MATH] Mathematics [math]"]}