Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-19T05:08:32.309Z Has data issue: false hasContentIssue false
  • English
  • Français

Rational approximations to algebraic numbers

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 by Roth in a recent paper that if α is any real algebraic number, and if K > 2, then the inequality

has only a finite number of solutions in relatively prime integers p, q (q > 0) The object of the present paper is to prove that the lower bound for κ can be reduced if conditions are imposed on p and q. The result obtained is as follows.

Type
Research Article
Information
Mathematika , Volume 4 , Issue 2 , December 1957 , pp. 125 - 131
Copyright
Copyright © University College London 1957

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

page 126 note † For references, see the preceding paper of Prof. Mahler.