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On the dimensions of quadratic forms.
2000According to Arason-Pfister's Hauptsatz the dimension of an anisotropic quadratic form in the \(n\)-th power \(I^n(k)\) of the fundamental ideal \(I(k)\) of the Witt ring \(W(k)\) is at least \(2^n\). The main result of the present paper is that, for any field \(k\) of characteristic zero, if the dimension of an anisotropic form in \(I^n(k)\) is ...
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Representation of Quadratic Forms by Integral Quadratic Forms
2013The number of representations of a positive definite integral quadratic form of rank n by another positive definite integral quadratic form of rank m ≥ n has been studied by arithmetic, analytic, and ergodic methods. We survey and compare in this article the results obtained by these methods.
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Proceedings of the London Mathematical Society, 1959
Davenport, Harold, Ridout, D.
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Davenport, Harold, Ridout, D.
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Quadratic forms and quadratic fields
1991Dedekind realised that one can give a clear presentation of Gauss’s theory of quadratic forms (Chapter 2), and particularly the composition of classes of forms, when one goes from forms to modules in quadratic fields. Here we consider the modules first and then give the connection between modules and forms.
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A necessary condition for the minimum of a quadratic form under rearrangements
Applied Mathematics Letters, 1995Tzon-Tzer Lu, Sui Sun Cheng
exaly