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The distribution of genera among quadratic spaces over global fields

Published online by Cambridge University Press:  14 November 2011

A. G. Earnest
A. G. Earnest
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901-4408, U.S.A
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Synopsis

For a Hasse domain R in a global field F, the distribution of genera of R-lattices with specified invariants among the nonisometric quadratic spaces over F which contain them is studied. It is shown that such genera are equally distributed for spaces of dimension 2, but that this is not generally the case for spaces of dimension exceeding 2. Theresult in the binary case yields an extension of a dimension exceeding 2. The result in the binary case yields an extension of a theorem of Gauss.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 2 , 1993 , pp. 391 - 397
Copyright
Copyright © Royal Society of Edinburgh 1993

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