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Bounds for the solutions of the hyperelliptic equation

Published online by Cambridge University Press:  24 October 2008

A. Baker
A. Baker
Affiliation:
Trinity College, Cambridge
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Extract

The purpose of this note is to extend the result which I established recently (see (3)) on the Diophantine equation

to some further equations of a similar kind. The following theorems will be proved.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 2 , March 1969 , pp. 439 - 444
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Baker, A.Contributions to the theory of Diophantine equations: I. On the representation of integers by binary forms. Philos. Trans. Roy. Soc. London Ser. A. 263 (1968), 173–191.Google Scholar
(2)Baker, A.Contributions to the theory of Diophantine equations: II. The Diophantine equation y 2 = x 2 + k. Philos. Trans. Roy. Soc. London Ser. A. 263 (1968), 193–208.Google Scholar
(3)Baker, A.The Diophantine equation y 2 = ax 3 + bx 2 + cx + d. J. London Math. Soc. 43 (1968), 1–9. (Dedicated to Prof. L. J. Mordell on his 80th birthday).CrossRefGoogle Scholar
(4)Hecke, E.Theorie der algebraischen Zahlen (Leipzig, 1923).Google Scholar
(5)Landau, E.Einführung in die elementare und analytische Theorie der algebraischen Zahlen und der Ideale (Leipzig and Berlin, 1927).Google Scholar
(6)Siegel, C. L.Approximation algebraischer Zahlen. Math. Z. 10 (1921), 173–213.CrossRefGoogle Scholar
(7)Siegel, C. L.(under the pseudonym X). The integer solutions of the equation J. London Math. Soc. 1 (1926), 66–68; = Ges. Abhandlungen I, 207–208.Google Scholar