Density theorems for GL(n)

• 成果类型: Article
• 署名作者: Blomer, Valentin
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01172-3
• 发表日期: 2023
• 页码: 683-711
• 关键词: kuznetsov formula; mellin transforms; conductor

摘要

Strong bounds-going beyond Sarnak's density hypothesis-are obtained for the number of automorphic forms for the group Gamma(0)(q) subset 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.