A CENTRAL LIMIT THEOREM FOR THE ZEROES OF THE ZETA FUNCTION

作者：Rodgers Brad^*

来源：International Journal of Number Theory, 2014, 10(2): 483-511.

DOI：10.1142/S1793042113501054

• Riemann zeta function
• random matrix theory
• central limit theorem

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 Spohn and 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.

• 出版日期2014-3