Random polynomials, random matrices, and $L$-functions
数学物理
2009-11-11 v3 math.MP
数论
摘要
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.
引用
@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}
}
备注
Added background material. Final version. To appear in Nonlinearity