arXiv:1111.4428 Abstract | arXiv Analytics

arXiv:1111.4428 [math.NT]Abstract References Reviews Resources

Density of values of linear maps on quadratic surfaces

Published 2011-11-18, updated 2013-01-29Version 3

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.

Comments: 15 pages, minor changes from version 2

Categories: math.NT

Subjects: 11J25, 37A17

Keywords: quadratic surface, linear map subject, integer points, algebraic conditions, quadratic form

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