Polynomial effective density in quotients of H3 and H2 x H2

• 成果类型: Article
• 署名作者: Lindenstrauss, E.; Mohammadi, A.
• 署名单位: Hebrew University of Jerusalem; University of California System; University of California San Diego
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01162-5
• 发表日期: 2023
• 页码: 1141-1237
• 关键词: effective equidistribution; homogeneous spaces; horocycle flow; Orbits; bounds; distributions; SUBGROUPS; points; BEHAVIOR

摘要

We prove effective density theorems, with a polynomial error rate, for orbits of the upper triangular subgroup of SL2(R) in arithmetic quotients of SL2(C) and SL2(R) x SL2(R). The proof is based on the use of a Margulis function, tools from incidence geometry, and the spectral gap of the ambient space.