New York Journal of Mathematics
Volume 3A (1997-1998) 69-80


Karma Dajani and Cor Kraaikamp

A Note on the Approximation by Continued Fractions under an Extra Condition

Published: March 2, 1998
Keywords: continued fractions, natural extension, skew-product
Subject: 28D05, 11K50

In this note the distribution of the approximation coefficients Θn, associated with the regular continued fraction expansion of numbers x∈ [0,1), is given under extra conditions on the numerators and denominators of the convergents pn/qn. Similar results are also obtained for S-expansions. Further, a Gauss-Kusmin type theorem is derived for the regular continued fraction expansion under these extra conditions.

Author information

Karma Dajani:
Universiteit Utrecht, Department of Mathematics, Budapestlaan 6, P.O.Box 80.000, 3508 TA Utrecht, the Netherlands

Cor Kraaikamp:
Thomas Stieltjes Institute for Mathematics and Technische Universiteit Delft, Faculty ITS, Department of Mathematics (SSOR), Mekelweg 4, 2628 CD Delft, the Netherlands