Heights and quadratic forms: on Cassels' theorem and its generalizations
Number Theory
2013-01-16 v1
Abstract
In this survey paper, we discuss the classical Cassels' theorem on existence of small-height zeros of quadratic forms over Q and its many extensions, to different fields and rings, as well as to more general situations, such as existence of totally isotropic small-height subspaces. We also discuss related recent results on effective structural theorems for quadratic spaces, as well as Cassels'-type theorems for small-height zeros of quadratic forms with additional conditions. We conclude with a selection of open problems.
Cite
@article{arxiv.1204.1938,
title = {Heights and quadratic forms: on Cassels' theorem and its generalizations},
author = {Lenny Fukshansky},
journal= {arXiv preprint arXiv:1204.1938},
year = {2013}
}
Comments
16 pages; to appear in the proceedings of the BIRS workshop on "Diophantine methods, lattices, and arithmetic theory of quadratic forms", to be published in the AMS Contemporary Mathematics series