Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4593839 | Journal of Number Theory | 2014 | 22 Pages |
Abstract
In this paper we investigate the density properties of the set of values of a linear map at integer points on a quadratic surface. In particular we show that this set is dense in the range of the linear map subject to certain algebraic conditions on the linear map and the quadratic form that defines the surface. The proof uses Ratner's theorem on orbit closures of unipotent subgroups acting on homogeneous spaces.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Oliver Sargent,