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The p-adic generalization of the Thue-Siegel-Roth theorem

Published online by Cambridge University Press:  26 February 2010

D. Ridout
D. Ridout
Affiliation:
Department of Mathematics, University College, London.
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Extract

It was proved recently by Roth that if α is any real algebraic number, and κ > 2, then the inequality

has only a finite number of solutions in integers h and q, where q > 0 and (h, q) = 1. This remarkable result answered finally a question which had been only partially answered by the work of Thue and Siegel.

Type
Research Article
Information
Mathematika , Volume 5 , Issue 1 , June 1958 , pp. 40 - 48
Copyright
Copyright © University College London 1958

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References

page 40 note † Mathematika, 2 (1955), 1–20. This paper will be referred to as R.CrossRefGoogle Scholar

page 40 note ‡ Math. Annalen, 107 (1933), 691–730.CrossRefGoogle Scholar

page 40 note § See, for example, Waerden, van der, Moderne Algebra I (New York, 1953), 235–243.Google Scholar

page 41 note † Loc. cit., Hilfsatz 5 and §18.

page 41 note ‡ Math. Annalen, 108 (1933), 37–55.

page 47 note ‡ Mahler, lco. cit., 701.