{"docId":139,"paperId":139,"url":"https:\/\/hrj.episciences.org\/139","doi":"10.46298\/hrj.1999.139","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":33,"name":"Volume 22 - 1999"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01109602","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01109602v1","dateSubmitted":"2015-03-03 16:13:52","dateAccepted":"2015-06-12 16:05:42","datePublished":"1999-01-01 08:00:00","titles":{"en":"Notes on the Riemann zeta Function-III"},"authors":["Balasubramanian, R","Ramachandra, K","Sankaranarayanan, A","Srinivas, K"],"abstracts":{"en":"For a good Dirichlet series $F(s)$ (see Definition in \\S1) which is a quotient of some products of the translates of the Riemann zeta-function, we prove that there are infinitely many poles $p_1+ip_2$ in $\\Im (s)>C$ for every fixed $C>0$. Also, we study the gaps between the ordinates of the consecutive poles of $F(s)$."},"keywords":[{"en":" mean-value"},{"en":" short-intervals"},{"en":" maximum-modulus principle"},{"en":" Hadamard three circles theorem"},{"en":" Ingham lines"},{"en":" Dirichlet series"},{"en":"Poles"},"[MATH] Mathematics [math]"]}