{"docId":5110,"paperId":5110,"url":"https:\/\/hrj.episciences.org\/5110","doi":"10.46298\/hrj.2019.5110","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01986703","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01986703v1","dateSubmitted":"2019-01-23 14:18:03","dateAccepted":"2019-01-23 15:34:48","datePublished":"2019-01-23 15:35:00","titles":{"en":"On certain sums over ordinates of zeta-zeros II"},"authors":["Bondarenko\n, \nAndriy","Ivi\u0107\n, \nAleksandar","Saksman\n, \nEero","Seip\n, \nKristian"],"abstracts":{"en":"Let \u03b3 denote the imaginary parts of complex zeros \u03c1 = \u03b2 + i\u03b3 of \u03b6(s). The problem of analytic continuation of the function $G(s) :=\\sum_{\\gamma >0} {\\gamma}^{-s}$ to the left of the line $\\Re{s} = \u22121 $ is investigated, and its Laurent expansion at the pole s = 1 is obtained. Estimates for the second moment on the critical line $\\int_{1}^{T} {| G (\\frac{1}{2} + it) |}^2 dt $ are revisited. This paper is a continuation of work begun by the second author in [Iv01]."},"keywords":[{"en":"2010 Mathematics Subject Classification 11M06 Keywords Riemann zeta-function"},{"en":"Riemann hypothesis"},{"en":"analytic continuation"},{"en":"Laurent expansion"},{"en":"second moment"},"\n[\nMATH\n] \nMathematics [math]","\n[\nMATH.MATH-NT\n] \nMathematics [math]\/Number Theory [math.NT]"]}