On the representations of numbers by binary cubic forms
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This article is published in Glasgow Mathematical Journal.The article was published on 1985-10-01 and is currently open access. It has received 4 citations till now. The article focuses on the topics: Binary number.read more
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On Thue's equation
TL;DR: The first important results on the number of primitive solutions of Thue's equation were obtained by C.L. Siegel as mentioned in this paper, in the case r = 3 and in the binomial case F (x, y ) = a x r b y r. In view of Siegel's results and comments, we should attribute to Siegel the problem to decide whether the number for primitive solutions to (1.1), for irreducible F of degree r > 3, could be bounded by a function depending only on r and h.
Journal Article
On binary quartic forms.
TL;DR: In this article, it was shown that for all binary cubics with determinants equal to minus thrice a perfect square, it is exceptional for a number represented by / to be represented more than essentially once.
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The addition of binary cubic forms
Jörg Brüdern,Trevor D. Wooley +1 more
TL;DR: In this paper, it was shown that a sum of four non-degenerate binary cubic forms with integral coefficients necessarily possesses a non-trivial rational zero, and that almost all integers, lying in those congruence classes permitted by local solubility conditions, are represented as the sum of the aforementioned forms.
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On the rational points on cubic surfaces
TL;DR: In this paper, it was shown that the number of solutions of the indeterminate ax-3+by-by-ax-3 equation is polynomial in the size of the projective surface defined by the equation.
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