Local analysis of the Kuznetsov formula and the density conjecture
Number Theory
2024-04-09 v1
Abstract
We prove Sarnak's spherical density conjecture for the principal congruence subgroup of SL(n, Z) of arbitrary level. Applications include a complete version of Sarnak's optimal lifting conjecture for principal congruence subgroups of SL(n, Z), as well as a transfer of the density theorem to certain co-compact situations. The main ingredients are new lower bounds for Whittaker functions and strong estimates for the cardinality of ramified Kloosterman sets.
Keywords
Cite
@article{arxiv.2404.05561,
title = {Local analysis of the Kuznetsov formula and the density conjecture},
author = {Edgar Assing and Valentin Blomer and Paul D. Nelson},
journal= {arXiv preprint arXiv:2404.05561},
year = {2024}
}
Comments
48 pages