A CENTRAL LIMIT THEOREM FOR THE ZEROES OF THE ZETA FUNCTION

Brad Rodgers

Type: Article

Publication Date: 2013-08-22

Citations: 12

DOI: https://doi.org/10.1142/s1793042113501054

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.

Locations

International Journal of Number Theory - View
arXiv (Cornell University) - View - PDF
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