, Volume 121, Issue 3, pp 213-229

On the error term in the mean square formula for the Riemann zeta-function in the critical strip

Abstract

For 1/2<σ<1 fixed, letE σ(T) denote the error term in the asymptotic formula for \(\int_0^T {|\zeta (\sigma + it)|^2 dt} \) . We obtain some new bounds forE σ(T), and an Ω_-result which is the analogue of the strongest Ω_-result in the classical Dirichlet divisor problem.