{"docId":169,"paperId":169,"url":"https:\/\/hrj.episciences.org\/169","doi":"10.46298\/hrj.2010.169","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":44,"name":"Volume 33 - 2010"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01112386","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01112386v1","dateSubmitted":"2015-03-03 16:14:03","dateAccepted":"2015-06-12 16:06:00","datePublished":"2010-01-01 08:00:00","titles":{"en":"An estimate for the Mellin transform of powers of Hardy's function."},"authors":["Jutila, Matti"],"abstracts":{"en":"We show that a certain modified Mellin transform $\\mathcal M(s)$ of Hardy's function is an entire function. There are reasons to connect $\\mathcal M(s)$ with the function $\\zeta(2s-1\/2)$, and then the orders of $\\mathcal M(s)$ and $\\zeta(s)$ should be comparable on the critical line. Indeed, an estimate for $\\mathcal M(s)$ is proved which in the particular case of the critical line coincides with the classical estimate of the zeta-function."},"keywords":[{"en":" Hardy's function"},{"en":"Riemann's zeta-function"},{"en":" Mellin transform"},"[MATH] Mathematics [math]"]}