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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.
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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.

Information

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

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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.