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Cubic forms representing arithmetic progressions

Published online by Cambridge University Press:  24 October 2008

G. L. Watson
G. L. Watson
Affiliation:
University CollegeLondon
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Extract

The following result has recently been proved by Lewis (3), Davenport (2) and Birch (1).

There exists an integer n0 such that every cubic form with rational coefficients and at least n0 integral variables represents zero non-trivially.

The arguments of Lewis and Birch are simple, and yield also various generalizations of this result. Davenport's proof is complicated, but it shows that the minimal n0 satisfies

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 3 , July 1959 , pp. 270 - 273
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

REFERENCES

(1)Birch, B. J.Mathematika 4 (1957), 102–5.CrossRefGoogle Scholar
(2)Davenport, H.Phil. Trans. A (in the Press).Google Scholar
(3)Lewis, D.Mathematika 4 (1957), 97–101.CrossRefGoogle Scholar
(4)Watson, G. L.Mathematika 1 (1954), 104–10.CrossRefGoogle Scholar
(5)Watson, G. L.Mathematika 2 (1955), 32–8.CrossRefGoogle Scholar