The Riemann Zeta-Function and the Sine Kernel
Number Theory
2008-09-05 v2 Mathematical Physics
math.MP
Abstract
We point out an interesting occurrence of the sine kernel in connection with the shifted moments of the Riemann zeta function along the critical line. We discuss rigorous results in this direction for the shifted second moment and for the shifted fourth moment. Furthermore, we conjecture that the sine kernel also occurs in connection with the higher (even) shifted moments and show that this conjecture is closely related to a recent conjecture by Conrey, Farmer, Keating, Rubinstein, and Snaith.
Cite
@article{arxiv.0803.1141,
title = {The Riemann Zeta-Function and the Sine Kernel},
author = {H. Kösters},
journal= {arXiv preprint arXiv:0803.1141},
year = {2008}
}
Comments
18 pages; revised version; references added