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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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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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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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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 Multivariate Hermitian Quadratic Forms
Mathematics in Computer Science, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ryoya Fukasaku +2 more
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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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