On the rate of convergence of distributions of random variables (Q542324)

Uniform estimates for the closeness of two distribution functions are obtained. Even moments of these functions are closed. The rate of the convergence to a limit distribution has the form: \[ O((\ln\ln\ln\ln T)/\sqrt{\ln\ln\ln T}). \] This estimate for the distribution of the arguments of the Riemann zeta-function is substantially better than the estimate obtained by \textit{M. A. Korolev} and \textit{A. A. Karatsuba} [Russ. Math. Surv. 61, No. 3, 389--482 (2006); translation from Usp. Mat. Nauk 61, No. 3, 3--92 (2006; Zbl 1215.11081)].