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

hrj:5110 - Hardy-Ramanujan Journal, January 23, 2019
On certain sums over ordinates of zeta-zeros II

Authors: Bondarenko , Andriy and Ivić , Aleksandar and Saksman , Eero and Seip , Kristian

Let γ denote the imaginary parts of complex zeros ρ = β + iγ of ζ(s). The problem of analytic continuation of the function $G(s) :=\sum_{\gamma >0} {\gamma}^{-s}$ to the left of the line $\Re{s} = −1 $ 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].


Source : oai:HAL:hal-01986703v1
Published on: January 23, 2019
Submitted 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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