Integer points on spheres and their orthogonal lattices

• 成果类型: Article
• 署名作者: Aka, Menny; Einsiedler, Manfred; Shapira, Uri
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; Technion Israel Institute of Technology
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0655-7
• 发表日期: 2016
• 页码: 379-396
• 关键词: FORMS; weight

摘要

Linnik proved in the late 1950's the equidistribution of integer points on large spheres under a congruence condition. The congruence condition was lifted in 1988 by Duke (building on a break-through by Iwaniec) using completely different techniques. We conjecture that this equidistribution result also extends to the pairs consisting of a vector on the sphere and the shape of the lattice in its orthogonal complement. We use a joining result for higher rank diagonalizable actions to obtain this conjecture under an additional congruence condition.