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On the Product of Three Homogeneous Linear Forms
Journal of the London Mathematical Society, 1938openaire +3 more sources
Note on the Product of Three Homogeneous Linear Forms
Journal of the London Mathematical Society, 1941openaire +4 more sources
The Product of Three Homogeneous Linear Ternary Forms
Journal of the London Mathematical Society, 1942openaire +4 more sources
On the product of three homogeneous linear forms
Mathematical Proceedings of the Cambridge Philosophical Society, 1951Let X denote the general point with coordinates (x1, x2, x3) in 3-dimensional space; and let P(X) be the function defined ...
Chalk, John H. H., Rogers, C. A.
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On the product of three homogeneous linear forms and indefinite ternary quadratic forms
Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1955Abstract Isolation theorems for the minima of factorizable homogeneous ternary cubic forms and of indefinite ternary quadratic forms of a new strong type are proved. The problems whether there exist such forms with positive minima other than multiples of forms with integer coefficients are shown to be equivalent to problems in the ...
Cassels, J. W. S. +1 more
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On the Product of Three Homogeneous Linear Forms. IV
Mathematical Proceedings of the Cambridge Philosophical Society, 1938Let L1, L2, L3 be three homogeneous linear forms in u, v, w with real coefficients and determinant 1. Let M denote the lower bound offor integral values of u, v, w, not all zero. I proved a few years ago (1) thatmore precisely, thatexcept when L1, L2, L3 are of a special type, in which case If we denote by θ, ø, ψ the roots of the cubic equation t3+t2-
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On the product of three non-homogeneous linear forms
Mathematical Proceedings of the Cambridge Philosophical Society, 1951Let ξ, η, ζ be linear forms in u, v, w with real coefficients and determinant Δ ≠ 0. Then there exists a number ℳ such that, corresponding to any real numbers a, b, c, there exist rational integers u, v, w for ...
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On the product of three non-homogeneous linear forms
Mathematical Proceedings of the Cambridge Philosophical Society, 1947Let ξ, η, ζ be linear forms inu, v, wwith real coefficients and determinant Δ ≠ 0. A conjecture of Minkowski, which was subsequently proved by Remak, tells us that for any real numbersa, b, cthere exist integral values ofu, v, wfor whichand the constant ⅛ on the right is best possible.
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