Local-global principles for representations of quadratic forms

• 成果类型: Article
• 署名作者: Ellenberg, Jordan S.; Venkatesh, Akshay
• 署名单位: University of Wisconsin System; University of Wisconsin Madison; New York University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-007-0077-7
• 发表日期: 2008
• 页码: 257-279
• 关键词: invariant-measures; lattice points; Integers; PROOF

摘要

We prove a local-global principle for the problem of representations of quadratic forms by quadratic forms over Z, in codimension >= 5. The proof uses the ergodic theory of p-adic groups, together with a fairly general observation on the structure of orbits of an arithmetic group acting on integral points of a variety.