Density theorems for $${\textrm{GL}}(n)$$-Reference-Cited by-同舟云学术

Density theorems for $${\textrm{GL}}(n)$$

Published:2022-11-20 Issue:2 Volume:232 Page:683-711
ISSN:0020-9910
Container-title:Inventiones mathematicae
language:en
Short-container-title:Invent. math.

Author:

Blomer Valentin

Abstract

AbstractStrong bounds—going beyond Sarnak’s density hypothesis—are obtained for the number of automorphic forms for the group

$$\Gamma _0(q) \subseteq \textrm{SL}(n, {\mathbb {Z}})$$

Γ 0 ( q ) ⊆ SL ( n , Z ) violating the Ramanujan conjecture at any given unramified place. The proof is based on a relative trace formula of Kuznetsov type and best-possible bounds for certain Kloosterman sums for

$$\textrm{GL}(n)$$

GL ( n ) . Further applications are given.

Funder

Rheinische Friedrich-Wilhelms-Universität Bonn

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s00222-022-01172-3.pdf

Reference35 articles.

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2. Assing, E., Blomer, V.: The density conjecture for principal congruence subgroups. arXiv:2204.08868

3. Blomer, V.: Applications of the Kuznetsov formula on $${\rm GL}(3)$$. Invent. Math. 194, 673–729 (2013)

4. Blomer, V., Brumley, F.: The role of the Ramanujan conjecture in analytic number theory. Bull. Am. Math. Soc. 50, 267–320 (2013)

5. Blomer, V., Buttcane, J., Maga, P.: Applications of the Kuznetsov formula on $${\rm GL}(3)$$: the level aspect. Math. Ann. 369, 723–759 (2017)

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