Atkinson's formula for the mean square of ζ(s) with an explicit error term

Abstract

We provide an explicit O(log2⁡T)-term of the celebrated Atkinson's formula for the error term E(T) of the second power moment of the Riemann zeta-function on the critical line. As an application, we obtain an explicit version of well-known estimate E(T)≪εT13+ε.