Bounds for integral solutions of diagonal cubic equations

Author:

Leung Ka Hin

Abstract

It was proved by Davenport [3] that for the nonzero integral λ i {\lambda _i} the equation λ 1 x 1 3 + + λ 8 x 8 3 = 0 {\lambda _1}x_1^3 + \cdots + {\lambda _8}x_8^3 = 0 always has a nontrivial integral solution. In this paper, we investigate the bounds of nontrivial integral solutions in terms of λ 1 , , λ 8 {\lambda _1}, \ldots ,{\lambda _8} .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference10 articles.

1. On Waring’s problem for cubes;Davenport, H.;Acta Math.,1939

2. Indefinite quadratic forms in many variables;Davenport, H.;Mathematika,1956

3. Cubic forms in thirty-two variables;Davenport, H.;Philos. Trans. Roy. Soc. London Ser. A,1959

4. On indefinite quadratic forms in five variables;Davenport, H.;J. London Math. Soc.,1946

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