Equidistribution of values of linear forms on quadratic surfaces

Sargent, Oliver

doi:10.2140/ant.2014.8.895

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Equidistribution of values of linear forms on quadratic surfaces

Oliver Sargent

Vol. 8 (2014), No. 4, 895–932

DOI: 10.2140/ant.2014.8.895

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

Vol. 8, No. 4, 2014