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.

arXiv comment38 pages, Comments are always very welcome!

References in corpus (1)

• Extreme values of the Riemann zeta function and its argument

Cited by in corpus (4)

• Extreme values for iterated integrals of the logarithm of the Riemann zeta-function
• On the value-distribution of iterated integrals of the logarithm of the Riemann zeta-function II: probabilistic aspects
• On the value-distribution of iterated integrals of the logarithm of the Riemann zeta-function I: denseness
• Joint value distribution of $L$-functions on the critical line