{"docId":122,"paperId":122,"url":"https:\/\/hrj.episciences.org\/122","doi":"10.46298\/hrj.1991.122","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":25,"name":"Volume 14 - 1991"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01104792","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01104792v1","dateSubmitted":"2015-03-03 16:13:46","dateAccepted":"2015-06-12 16:05:31","datePublished":"1991-01-01 08:00:00","titles":{"en":"On the zeros of a class of generalised Dirichlet series-VIII"},"authors":["Balasubramanian, R","Ramachandra, K"],"abstracts":{"en":"In an earlier paper (Part VII, with the same title as the present paper) we proved results on the lower bound for the number of zeros of generalised Dirichlet series $F(s)= \\sum_{n=1}^{\\infty} a_n\\lambda^{-s}_n$ in regions of the type $\\sigma\\geq\\frac{1}{2}-c\/\\log\\log T$. In the present paper, the assumptions on the function $F(s)$ are more restrictive but the conclusions about the zeros are stronger in two respects: the lower bound for $\\sigma$ can be taken closer to $\\frac{1}{2}-C(\\log\\log T)^{\\frac{3}{2}}(\\log T)^{-\\frac{1}{2}}$ and the lower bound for the number of zeros is something like $T\/\\log\\log T$ instead of the earlier bound $>\\!\\!\\!>T^{1-\\varepsilon}$."},"keywords":[{"en":"Borel-Carath\\'eodory theorem"},{"en":"generalised Dirichlet series"},"[MATH] Mathematics [math]"]}