Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-27T22:33:48.466Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

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

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