Some identities for the Riemann zeta-function

2003/05/31 by Aleksandar Ivic
Mathematics · #math.NT #msc:11M06

paper · pdf

published as Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 14(2003), 20-25. · 6 pages, no changes; TeX settings corrected

arxiv created 2003/11/06 · arxiv updated 2009/11/30

Abstract

Several identities for the Riemann zeta-function ζ(s) are proved. For example, if s = σ+ it and σ> 0, then ∫_-∞^∞ |(1-2^1-s)ζ(s)\over s|²dt = π\overσ(1 - 2^1-2σ)ζ(2σ).

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