On matrix Kloosterman sums and Hall-Littlewood polynomials

Abstract

We prove an identity relating twisted matrix Kloosterman sums to modified Hall-Littlewood polynomials evaluated at the roots of the characteristic polynomial associated to a twisted Kloosterman sheaf. This solves a conjecture of Erdélyi and Tóth.

arXiv comment25 Pages, comments are welcome. v4: This version contains all changes that were made for submission in Transactions of the AMS

References in corpus (2)

• Traces of powers of matrices over finite fields
• Matrix Kloosterman sums