Random polynomials, random matrices, and $L$-functions
Mathematical Physics
2009-11-11 v3 math.MP
Number Theory
Abstract
We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.
Keywords
Cite
@article{arxiv.math-ph/0509044,
title = {Random polynomials, random matrices, and $L$-functions},
author = {David W Farmer and Francesco Mezzadri and Nina C Snaith},
journal= {arXiv preprint arXiv:math-ph/0509044},
year = {2009}
}
Comments
Added background material. Final version. To appear in Nonlinearity