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On a theorem of Davenport concerning continued fractions

Published online by Cambridge University Press:  26 February 2010

Michel Mendes France
Michel Mendes France
Affiliation:
Laboratoire de Mathématiques, et d'Informatique dépendant de, l'Université de Bordeaux I, 351, cours de la Libération, 33405 Talence.
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Extract

Several years ago, Davenport [2] noticed that for any real irrational number ξ and for any prime number p, one at least of the numbers

has infinitely many partial quotients larger than p – 2 in its continued fraction expansion.

Type
Research Article
Information
Mathematika , Volume 23 , Issue 2 , December 1976 , pp. 136 - 141
Copyright
Copyright © University College London 1976

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References

1.Billingsley, P.. Ergodic Theory and Information (John Wiley & Sons, 1965).Google Scholar
2.Davenport, H.. “A remark on continued fractions”, Michigan Math. Jour., 11 (1964), 343–344.Google Scholar
3.France, M. Mendes. “Sur les fractions continues limitees”, Ada Arith., 23 (1973), 207–215.CrossRefGoogle Scholar