The density conjecture for principal congruence subgroups

Abstract

We prove Sarnak's density conjecture for the principal congruence subgroup of SL_n(Z) of squarefree level and discuss various arithmetic applications. The ingredients include new bounds for local Whittaker functions and Kloosterman sums.

minor updates and different layout; to appear in Duke Math. J

Cited by in corpus (1)

• On the local $L^2$-Bound of the Eisenstein Series