The distribution of values of zeta and L-functions

Abstract

We survey recent progress on understanding the distribution of values of zeta and $L$-func­tions. In particular, we discuss the problem of moments of $|\zeta (\frac{1}{2}+it)|$ and moments of central $L$-values in families, where the last 25 years have seen a conjectural understanding of the asymptotics of these moments, together with progress in obtaining good upper and lower bounds in many situations.