On the Ramanujan conjecture over number fields

• 成果类型: Article
• 署名作者: Blomer, Valentin; Brumley, Farrell
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.174.1.18
• 发表日期: 2011
• 页码: 581-605
• 关键词: automorphic l-functions; square l-functions; exterior square; adic groups; REPRESENTATIONS; EIGENVALUE; FORMULA; poles; gl(2)

摘要

We extend to an arbitrary number field the best known bounds towards Ramanujan for the group GL(n), n = 2, 3, 4. In particular, we present a technique which overcomes the analytic obstacles posed by the presence of an infinite group of units.