An asymptotic expansion of Selberg's central limit theorem near the critical line

Abstract

We find an asymptotic expansion of Selberg's central limit theorem for the Riemann zeta function on $\sigma =\frac{1}{2}+(\log T{)}^{-\theta }$ and $t\in [T,2T]$, where $0<\theta <\frac{1}{2}$ is a constant.