Subconvexity for the Riemann zeta-function and the divisor problem

M. N. Huxley, A. Ivić

Published 2006-11-27, updated 2007-09-18Version 3

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.