A density theorem for Borel-Type Congruence subgroups and arithmetic applications

Abstract

We use a (pre)-Kuznetsov type formula to prove a density result for the Borel-type congruence subgroup of GLn. This has some arithmetic applications to optimal lifting and counting considered earlier by A. Kamber and H. Lavner for $G{L}_3$.

31 pages, corrections taking into account referee reports, to appear in Algebra and Number Theory