Artin-Schreier L-functions and Random Unitary Matrices

2013/08/14 by Entin, Alexei
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1308.3163

Abstract

We give a new derivation of an identity due to Z. Rudnick and P. Sarnak about the n-level correlations of eigenvalues of random unitary matrices as well as a new proof of a formula due to M. Diaconis and P. Shahshahani expressing averages of trace products over the unitary matrix ensemble. Our method uses the zero statistics of Artin-Schreier L-functions and a deep equidistribution result due to N. Katz and P. Sarnak.

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