On the estimation of Z₂(s)

2003/11/18 by Aleksandar Ivić
Mathematics · #math.NT #msc:11M06 #msc:11F72

paper · pdf

published as in "Anal. Probab. Methods Number Thery" (eds A. Dubickas et al.), TEV, Vilnius 2002, 83-98.

arxiv created 2003/11/18 · arxiv updated 2009/12/01

Abstract

Estimates for Z₂(s) = ∫₁^|infty |ζ(1/2+ix)|⁴x^-sdx (\Re s > 1) are discussed, both pointwise and in mean square. It is shown how these estimates can be used to bound E₂(T), the error term in the asymptotic formula for ∫₀^T |ζ(1/2+it)|⁴dt.

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