English

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.

Keywords

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

R2 v1 2026-06-24T10:52:06.386Z