English

Artin-Schreier L-functions and Random Unitary Matrices

Number Theory 2013-12-03 v3

Abstract

We give a new derivation of an identity due to Z. Rudnick and P. Sarnak about the nn-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.

Keywords

Cite

@article{arxiv.1308.3163,
  title  = {Artin-Schreier L-functions and Random Unitary Matrices},
  author = {Alexei Entin},
  journal= {arXiv preprint arXiv:1308.3163},
  year   = {2013}
}