On some conjectures and results for the Riemann zeta-function and Hecke series

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

paper · pdf

published as Acta Arithmetica 99(2001), 115-145

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

Abstract

Some results and conjectures on Z₂(s) = ∫₁^∞ |ζ(1/2+ix)|⁴x^-sdx (\Re s > 1) are presented. Consequences of these conjectures regarding the eighth moment of |ζ(1/2+it) and the error term in the fourth moment of |ζ(1/2+it) are discussed.

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