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Density theorems for GL(n)

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arxiv 1906.07459 v2 pith:B5MGA2TZ submitted 2019-06-18 math.NT

Valentin Blomer This is my paper · ORCID
classification math.NT
keywords boundsdensitygivenapplicationsautomorphicbest-possiblebeyondcertain
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Strong bounds - going beyond Sarnak's density hypothesis - are obtained for the number of automorphic forms for the congruence subgroup Gamma_0(q) of 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 GL(n). Further applications are given.

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  1. Optimal Lifting for the Projective Action of $SL_3(Z)$

    math.NT 2019-08 conditional novelty 8.0 of 10

    For almost all pairs of points in P^2(F_q), an element of SL3(Z) with entries bounded by q^{1/3+ε} realizes the projective action.

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