Lenny Fukshansky
Published 2012-04-09Version 1
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: 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
Journal: Contemporary Mathematics, AMS vol. 587 (2013), pg. 77--94
Algebraic functions with Fermat property, eigenvalues of transfer operator and Riemann zeros, and other open problems
Continued Fractions and Generalizations with Many Limits: A Survey
On two problems of Carlitz and their generalizations
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