The sup-norm problem for newforms of large level on PGL(n)

• 成果类型: Article
• 署名作者: Toma, Radu
• 署名单位: Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910; 1432-1297
• DOI: 10.1007/s00222-026-01409-5
• 发表日期: 2026-06
• 页码: 1093-1145
• 关键词: cusp forms; subconvexity; density; CURVES

摘要

Let N be a prime and phi be a Hecke-Maa ss cuspidal newform for the Hecke congruence subgroup Gamma 0(N) in SLn(R). We define a notion of the bulk Omega N of the space Gamma 0(N)\SLn(R)/SO(n) with respect to a compact set Omega subset of SLn(R). For any prime n, we prove sub-baseline bounds for the sup-norm of phi restricted to Omega N. Conditionally on GRH, we generalise this result to all n >= 2. The methods involve a new reduction theory with level structure, based on generalisations of Atkin-Lehner operators.