Andriy Bondarenko ; Aleksandar Ivić ; Eero Saksman ; Kristian Seip - On certain sums over ordinates of zeta-zeros II

hrj:5110 - Hardy-Ramanujan Journal, January 23, 2019 - https://doi.org/10.46298/hrj.2019.5110
On certain sums over ordinates of zeta-zeros IIArticle

Authors: Andriy Bondarenko 1; Aleksandar Ivić 2; Eero Saksman 1; Kristian Seip 1

Let γ denote the imaginary parts of complex zeros ρ = β + iγ of ζ(s). The problem of analytic continuation of the function G(s):=γ>0γs to the left of the line s=1 is investigated, and its Laurent expansion at the pole s = 1 is obtained. Estimates for the second moment on the critical line T1|G(12+it)|2dt are revisited. This paper is a continuation of work begun by the second author in [Iv01].


Published on: January 23, 2019
Imported on: January 23, 2019
Keywords: 2010 Mathematics Subject Classification 11M06 Keywords Riemann zeta-function,Riemann hypothesis,analytic continuation,Laurent expansion,second moment,[MATH]Mathematics [math],[MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]

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