Density of values of linear maps on quadratic surfaces

2011/11/18 by Oliver Sargent, Sargent, Oliver · 1 citation
Mathematics · #11J25 #37A17 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J25 #msc:37A17

paper · pdf · doi:10.48550/arxiv.1111.4428

15 pages, minor changes from version 2

arxiv created 2013/01/29 · arxiv updated 2013/01/30

Abstract

In this paper we investigate the distribution 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.

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