Subconvexity for the Riemann zeta-function and the divisor problem

Abstract

A simple proof of the classical subconvexity bound $ζ(1/2+it) \ll_εt^{1/6+ε}$ 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 $|ζ(1/2+it)|$ are analysed.