Subconvexity for the Riemann zeta-function and the divisor problem

Details Subconvexity for the Riemann zeta-function and the divisor problem Subconvexity for the Riemann zeta-function and the divisor problem

2006-11-27

arxiv.org/abs/math/0611809v3

Bulletin CXXXIV de l'Acad\'emie Serbe des Sciences et des Arts - 2007, Classe des Sciences math\'ematiques et naturelles, Scie

Mathematics

Number Theory

18 pages

Scientific paper

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.

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