Subconvexity for the Riemann zeta-function and the divisor problem

M. N. Huxley; A. Ivić

Subconvexity for the Riemann zeta-function and the divisor problem

Number Theory 2007-09-18 v3

Authors: M. N. Huxley , A. Ivić

Abstract

A simple proof of the classical subconvexity bound $\zeta(1/2+it) \ll_\epsilon t^{1/6+\epsilon}$ for the Riemann zeta-function is given, and estimation by more refined techniques is discussed. The connections between the Dirichlet divisor problem and the mean square of $|\zeta(1/2+it)|$ are analysed.

Keywords

riemann zeta function zeta functions zeta values and euler sums

Cite

@article{arxiv.math/0611809,
  title  = {Subconvexity for the Riemann zeta-function and the divisor problem},
  author = {M. N. Huxley and A. Ivić},
  journal= {arXiv preprint arXiv:math/0611809},
  year   = {2007}
}

Comments

18 pages

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