On certain sums over ordinates of zeta zeros

2003/12/16 by Aleksandar Ivić
Mathematics · #math.NT #msc:11M06

paper · pdf

published as Bull. CXXII Acad. Serbe Sciences Mathématiques No. 26(2001), 39-52 · 13 pages

arxiv created 2003/12/16 · arxiv updated 2009/12/01

Abstract

Let γ denote imaginary parts of complex zeros of the Riemann zeta-function ζ(s). Certain sums over the γ's are evaluated, by using the function G(s) = ∑_γ>0γ^-s and other techniques. Some integrals involving the function S(T) = (1/π)argζ(1/2+iT) are also considered.

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