Results 271 to 280 of about 49,024 (304)

A note on quadratic forms

Mathematical Programming, 1999
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Xin Chen, Ya-Xiang Yuan
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On the Theory of Quadratic Forms

The Annals of Mathematics, 1949
In this note we give an extention of the analytic theory of quadratic forms of C. L. Siegel'. We use the well-known matrix notation, if the contrary is not expressly mentioned we suppose the elements of all matrices to be rational integers. Let A(S, T; P, v) denote the number of solutions X of the Diophantic matrix equation X'SX = T, which satisfy the ...
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Simplicial Quadratic Forms

Canadian Journal of Mathematics, 1983
0. Introduction. Simplicial quadratic forms (cf. Definition 1.4), and various equivalent forms, have occasionally been studied in geometry [8], and in number theory [9], [10], in connection with the extremal properties of integral quadratic forms. Our investigations, which employ simple techniques from graph theory and geometry, partly continue both ...
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On the dimensions of quadratic forms.

2000
According 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

2013
The 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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Indefinite Quadratic Forms

Proceedings of the London Mathematical Society, 1959
Davenport, Harold, Ridout, D.
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Quadratic forms and quadratic fields

1991
Dedekind 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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On the Distribution of a Quadratic Form

Biometrika, 1970
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Simultaneous Quadratic Forms

American Journal of Mathematics, 1962
Birch, B. J., Lewis, D. J., Murphy, T. G.   +2 more
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Isotropy of quadratic forms over the function field of a quadric in characteristic 2

Journal of Algebra, 2006
Detlev W Hoffmann, Ahmed Laghribi
exaly