English

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!