Matrix Kloosterman sums modulo prime powers

Abstract

We give optimal bounds for matrix Kloosterman sums modulo prime powers extending earlier work of the first two authors on the case of prime moduli. These exponential sums arise in the theory of the horocyclic flow on ${\mathrm{GL}}_n$.

20 pages, v2: revised according to referee's comments, fixed an error in Prop. 3.4, v3: minor changes