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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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References

1Arenas, A.. Rational equivalence of primitive integral binary quadratic forms. Proc. Roy. Soc. Edinburgh Sect. A 118 (1991), 157–160.CrossRefGoogle Scholar
2Earnest, A. G.. Genera of rationally equivalent integral binary quadratic forms. Proc. Roy. Soc. Edinburgh Sect. A 119 (1991), 27–30.CrossRefGoogle Scholar
3Earnest, A. G. and Estes, D. R.. Class groups in the genus and spinor genus of binary quadratic lattices. Proc. London Math. Soc. 40 (1980), 40–52.CrossRefGoogle Scholar
4Gauss, C. F.. Disquisitiones Arithmeticae (New Haven: Yale University Press, 1966).Google Scholar
5James, D. G.. Even quadratic forms with cube-free discriminant. Proc. Amer. Math. Soc. 106 (1989), 73–79.CrossRefGoogle Scholar
6James, D. G.. Quadratic forms with cube-free discriminant. Proc. Amer. Math. Soc. 110 (1990), 45–52.CrossRefGoogle Scholar
7Körner, O. H.. Integral representations over local fields and the number of genera of quadratic forms. Ada Arith. 24 (1973), 301–311.Google Scholar
8O'Meara, O. T.. Introduction to Quadratic Forms (Berlin: Springer, 1963).CrossRefGoogle Scholar