Local analysis of the Kuznetsov formula and the density conjecture

Journal de Mathématiques Pures et Appliquées 2026 Open access

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Authors: Edgar Assing, Valentin Blomer, Paul D. Nelson
DOI: 10.1016/j.matpur.2026.103954
Cited by: 1
References: 54

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.

Fields of Study & Subjects

advanced mathematical theories Mathematical Dynamics and Fractals Graph theory and applications

Publication details

Journal / source
Journal de Mathématiques Pures et Appliquées
Publisher
Elsevier BV
Volume
214
Pages
103954–103954
Publication date
19 June 2026
Language
EN