The density conjecture for principal congruence subgroups
Number Theory
2023-07-13 v2 Representation Theory
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.
Cite
@article{arxiv.2204.08868,
title = {The density conjecture for principal congruence subgroups},
author = {Edgar Assing and Valentin Blomer},
journal= {arXiv preprint arXiv:2204.08868},
year = {2023}
}
Comments
minor updates and different layout; to appear in Duke Math. J