Abstract
We prove the spherical density conjecture of Sarnak for the principal subgroup of of square-free level and discuss various arithmetic applications. The ingredients include new bounds for local Whittaker functions and Kloosterman sums.
Citation
Edgar Assing. Valentin Blomer. "The density conjecture for principal congruence subgroups." Duke Math. J. 173 (7) 1359 - 1426, 15 May 2024. https://doi.org/10.1215/00127094-2023-0040
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