On certain sums over ordinates of zeta-zeros IIArticle
Authors: Andriy Bondarenko 1; Aleksandar Ivić 2; Eero Saksman 1; Kristian Seip 1
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Andriy Bondarenko;Aleksandar Ivić;Eero Saksman;Kristian Seip
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].
Published on: January 23, 2019
Imported on: January 23, 2019
Keywords: [MATH]Mathematics [math], [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], [en] 2010 Mathematics Subject Classification 11M06 Keywords Riemann zeta-function, Riemann hypothesis, analytic continuation, Laurent expansion, second moment
Funding:
Source : OpenAIRE Graph- Dirichlet Series and Analysis on Polydiscs; Funder: The Research Council of Norway; Code: 227768