On the Riemann zeta-function and the divisor problem II

2004/11/30 by Aleksandar Ivić
Mathematics · #math.NT #msc:11N37 #msc:11M06

paper · pdf

published as Central European Journal of Mathematics 3(2) (2005), 203-214 · 13 pages

arxiv created 2005/03/01 · arxiv updated 2009/12/01

Abstract

First part of this paper was published in CEJM (2)(4) (2004), 1-15. It is proved now that ∫₀^T|E^*(t)|⁵\rm dt ≪_εT^2+ε. Here E^*(t) = E(t) - 2πΔ^*(t/2π), Δ^*(x) = - Δ(x) +2Δ(2x) - 1\over2Δ(4x), where E(t) is the error term in the mean square formula for |ζ(1/2+it)| and Δ(x) is the error term in the Dirichlet divisor problem. It is also shown how bounds for moments of |E^*(t)| lead to bounds for moments of |ζ(1/2+it)|.

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