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
Cited by
3 articles.
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