On the logarithm of the Riemann zeta-function and its iterated integrals

Abstract

This paper gives some results for the logarithm of the Riemann zeta-function and its iterated integrals. We obtain a certain explicit approximation formula for these functions. The formula has some applications, which are related with the value distribution of these functions and a relation between prime numbers and the distribution of zeros in short intervals.

38 pages, Comments are always very welcome!