On the logarithm of the Riemann zeta-function and its iterated integrals
Number Theory
2019-12-11 v2
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.
Keywords
Cite
@article{arxiv.1909.03643,
title = {On the logarithm of the Riemann zeta-function and its iterated integrals},
author = {Shōta Inoue},
journal= {arXiv preprint arXiv:1909.03643},
year = {2019}
}
Comments
38 pages, Comments are always very welcome!