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arXiv · 1204.1938

Heights and quadratic forms: on Cassels' theorem and its generalizations

Lenny Fukshansky
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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.

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Lenny Fukshansky. 2012-04-09. Heights and quadratic forms: on Cassels' theorem and its generalizations. https://arxiv.org/abs/1204.1938

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