Search Bounds with Respect to Height in Linear and Quadratic Spaces

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Mathematics (CMC)

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In this talk, I will discuss a variety of results on existence of points and subspaces of bounded height, possibly satisfying some additional algebraic conditions, in linear and quadratic spaces over global fields and rings. These results represent some of the recent developments on extensions and generalizations of such classical Diophantine theorems as Siegel's lemma and Cassels' theorem on small zeros of quadratic forms.

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© 2011 Lenny Fukshansky

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