Subconvexity for the Riemann zeta-function and the divisor problem

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.

18 pages