Random polynomials, random matrices, and $L$-functions

Details Random polynomials, random matrices, and $L$-functions Random polynomials, random matrices, and $L$-functions

2005-09-20

arxiv.org/abs/math-ph/0509044v3

Nonlinearity 19 (2006) 919-936

Physics

Mathematical Physics

Added background material. Final version. To appear in Nonlinearity

Scientific paper

10.1088/0951-7715/19/4/008

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.

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