Spectral aspect subconvex bounds for Un+1 x Un

• 成果类型: Article
• 署名作者: Nelson, Paul D.
• 署名单位: Aarhus University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01180-x
• 发表日期: 2023
• 页码: 1273-1438
• 关键词: kuznetsov formula; REPRESENTATIONS; period; NORMS

摘要

Let (pi, sigma) traverse a sequence of pairs of cuspidal automorphic representations of a unitary Gan-Gross-Prasad pair (Un+1, U-n) over a number field, with Un anisotropic. We assume that at some distinguished archimedean place, the pair stays away from the conductor dropping locus, while at every other place, the pair has bounded ramification and satisfies certain local con-ditions (in particular, temperedness). We prove that the subconvex bound L(pi x sigma, 1/2) << C(pi x sigma )(1/4-delta) holds for any fixed delta < 1/8n(5) + 28n(4) + 42n(3) + 36n(2) + 14n . Among other ingredients, the proof employs a refinement of the microlocal calculus for Lie group representations developed with A. Venkatesh and an observation of S. Marshall concerning the geometric side of the relative trace formula.