A central limit theorem for the zeroes of the zeta function
Probability
2014-05-13 v5 Number Theory
Abstract
On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic interval. The result mirrors results of Soshnikov and others in random matrix theory. In an appendix we put forward some general theorems regarding our knowledge of the zeta zeroes in the mesoscopic regime.
Keywords
Cite
@article{arxiv.1205.0303,
title = {A central limit theorem for the zeroes of the zeta function},
author = {Brad Rodgers},
journal= {arXiv preprint arXiv:1205.0303},
year = {2014}
}
Comments
22 pages. Incorporates referees suggestions. Contains minor corrections to published version