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APPLICATIONS OF SYSTEMS OF QUADRATIC FORMS TO GENERALISED QUADRATIC FORMS
Bulletin of the Australian Mathematical Society, 2020A system of quadratic forms is associated to every generalised quadratic form over a division algebra with involution of the first kind in characteristic two. It is shown that this system determines the isotropy behaviour and the isometry class of generalised quadratic forms.
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Mathematical Programming, 1999
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Xin Chen, Ya-Xiang Yuan
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Xin Chen, Ya-Xiang Yuan
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Representation by Quadratic Forms
The Annals of Mathematics, 19491. Introduction. The elementary portions of the theory of integral representation of numbers or forms by quadratic forms will be somewhat simplified and generalized in this article. This indicates certain directions in which new applications can be made.
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On the Theory of Quadratic Forms
The Annals of Mathematics, 1949In 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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DISTRIBUTIONS OF QUADRATIC FORMS
Australian Journal of Statistics, 1988summaryExact expressions for the distribution function of a random variable of the form c1χ2m+c2χ2n are given where χ2m and χ2nχ2n are independent chi‐square random variables with m and n degrees of freedom respectively. (The positive ci are distinct).
Bock, Mary Ellen, Solomon, Herbert
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Proceedings of the London Mathematical Society, 1987
Let Q be a quadratic form, \(Q=L^ 2_ 1+... +L^ 2_ r-... -L^ 2_ n\) where \(L_ 1,...,L_ n\) are real linearly independent quadratic forms. If \(n=18\), \(r=9\); \(n=19\), \(8\leq r\leq 11\); or \(n=20\), \(7\leq r\leq 13\), then we can solve \(| Q(x)| 0\). This extends work of Davenport, Birch and Ridout.
Baker, R. C., Schlickewei, H. P.
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Let Q be a quadratic form, \(Q=L^ 2_ 1+... +L^ 2_ r-... -L^ 2_ n\) where \(L_ 1,...,L_ n\) are real linearly independent quadratic forms. If \(n=18\), \(r=9\); \(n=19\), \(8\leq r\leq 11\); or \(n=20\), \(7\leq r\leq 13\), then we can solve \(| Q(x)| 0\). This extends work of Davenport, Birch and Ridout.
Baker, R. C., Schlickewei, H. P.
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Inventiones mathematicae, 2005
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Noga Alon +3 more
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Journal of the London Mathematical Society, 1983
Let \(k\) be a fixed algebraically closed field. The author associates to each basic \(k\)-algebra \(A\), whose ordinary quiver \(Q\) has no oriented cycles, a quadratic form, called its Tits form, as follows: Denote by \(Q_ 0\) and \(Q_ 1\) the sets of vertices and arrows of \(Q\) respectively and by \(S_ i\) the simple \(A\)-module corresponding to ...
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Let \(k\) be a fixed algebraically closed field. The author associates to each basic \(k\)-algebra \(A\), whose ordinary quiver \(Q\) has no oriented cycles, a quadratic form, called its Tits form, as follows: Denote by \(Q_ 0\) and \(Q_ 1\) the sets of vertices and arrows of \(Q\) respectively and by \(S_ i\) the simple \(A\)-module corresponding to ...
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Canadian Journal of Mathematics, 1952
Hermite [4] in the course of his investigations on the transformation theory of abelian functions, introduced the notion of abelian quadratic forms. They are quadratic forms whose matrices of orders 2n, satisfywhere k ≠ 0 is a real number, and is the unit matrix of order n.
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Hermite [4] in the course of his investigations on the transformation theory of abelian functions, introduced the notion of abelian quadratic forms. They are quadratic forms whose matrices of orders 2n, satisfywhere k ≠ 0 is a real number, and is the unit matrix of order n.
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The Annals of Mathematics, 1952
?1. Let (E be the matrix of a quadratic form with rational integral coefficients and F (e) the group of integral solutions U of 25 [U] = U'2U = S. The group F (e) is called the unit group of (E and its elements the units of S. Eisenstein defined the measure of F (5), when (E is definite, as the reciprocal of the order of F (S).
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?1. Let (E be the matrix of a quadratic form with rational integral coefficients and F (e) the group of integral solutions U of 25 [U] = U'2U = S. The group F (e) is called the unit group of (E and its elements the units of S. Eisenstein defined the measure of F (5), when (E is definite, as the reciprocal of the order of F (S).
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