Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T21:03:17.445Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.