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On certain sums over ordinates of zeta-zeros II

Abstract : 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].
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Submitted on : Saturday, January 19, 2019 - 8:09:39 AM
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Andriy Bondarenko, Aleksandar Ivić, Eero Saksman, Kristian Seip. On certain sums over ordinates of zeta-zeros II. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2019, Atelier Digit_Hum, pp.85 - 97. ⟨10.46298/hrj.2019.5110⟩. ⟨hal-01986703⟩

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