Heights and Quadratic Forms: Cassels’ Theorem and its Generalizations

Authors

Lenny Fukshansky, Claremont McKenna CollegeFollow

Document Type

Article

Department

Mathematics (CMC)

Publication Date

2013

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.

Comments

Please note that this article was first published in Contemporary Mathematics 587 (2013) by the American Mathematical Society.

Rights Information

© 2013 American Mathematical Society

Recommended Citation

Fukshansky, Lenny. "Heights and Quadratic Forms: Cassels’ Theorem and its Generalizations." Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms. Contemporary Mathematics 587 (2013): 77-94.