{"docId":147,"paperId":147,"url":"https:\/\/hrj.episciences.org\/147","doi":"10.46298\/hrj.2003.147","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":37,"name":"Volume 26 - 2003"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01109810","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01109810v1","dateSubmitted":"2015-03-03 16:13:55","dateAccepted":"2015-06-12 16:05:47","datePublished":"2003-01-01 08:00:00","titles":{"en":"Mean-square upper bound of Hecke $L$-functions on the critical line."},"authors":["Sankaranarayanan, A"],"abstracts":{"en":"We prove the upper bound for the mean-square of the absolute value of the Hecke $L$-functions (attached to a holomorphic cusp form) defined for the congruence subgroup $\\Gamma_0 (N)$ on the critical line uniformly with respect to its conductor $N$."},"keywords":[{"en":" Holomorphic cusp forms"},{"en":" Mean-value theorems"},{"en":" Montgomery-Vaughan Theorem"},{"en":"Hecke $L$-functions"},"[MATH] Mathematics [math]"]}