Artin-Schreier L-functions and random unitary matrices

Alexei Entin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)340-351
Number of pages12
JournalJournal of Number Theory
Volume145
DOIs
StatePublished - Dec 2014

Funding

FundersFunder number
FP7/2007
European Research Council320755
Seventh Framework Programme

    Keywords

    • L-functions
    • Random matrix theory

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