Extreme values for iterated integrals of the logarithm of the Riemann zeta-function

Abstract

In this paper, we give an approximate formula for the measure of extreme values for the logarithm of the Riemann zeta-function and its iterated integrals. The result recovers the unconditional best result for the $\Omega$-result of $S_{1}(t)$ for the part of minus of Tsang.