Vol. 8, No. 4, 2014

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Equidistribution of values of linear forms on quadratic surfaces

Oliver Sargent

Vol. 8 (2014), No. 4, 895–932
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, it is shown that, subject to certain algebraic conditions, this set is equidistributed. This can be thought of as a quantitative version of the main result from a previous paper. The methods used are based on those developed by A. Eskin, S. Mozes and G. Margulis. Specifically, they rely on equidistribution properties of unipotent flows.

Keywords
quadratic forms, linear maps, integral values, unipotent flows
Mathematical Subject Classification 2010
Primary: 11E99
Secondary: 37A17, 37A45
Milestones
Received: 5 March 2013
Revised: 10 December 2013
Accepted: 22 January 2014
Published: 10 August 2014
Authors
Oliver Sargent
Department of Mathematics
University of Bristol
University Walk
Bristol
BS8 1TW
United Kingdom