Artin-Schreier L-functions and random unitary matrices

作者：Entin Alexei^*

来源：Journal of Number Theory, 2014, 145: 340-351.

DOI：10.1016/j.jnt.2014.06.019

• L-functions
• Random matrix theory

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.

• 出版日期2014-12