Matrix Kloosterman sums

Abstract

We study a family of exponential sums that arises in the study of the horocyclic flow on ${\mathrm{GL}}_n$. We prove an explicit version of general purity and find optimal bounds for these sums.

arXiv comment57 pages, some minor changes done and new references added

References in corpus (2)

• The asymptotic distribution of Frobenius numbers
• Equidistribution of primitive rational points on expanding horospheres

Cited by in corpus (1)

• On matrix Kloosterman sums and Hall-Littlewood polynomials