Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T05:08:06.833Z Has data issue: false hasContentIssue false

Continuants with bounded digits

Published online by Cambridge University Press:  26 February 2010

T. W. Cusick
Affiliation:
State University of New York at Buffalo.
Get access

Extract

We let K(a1a2, ak) denote the continuant formed from the positive integers a1 …, ak; that is,

Of course, K(a1, …, an) is the denominator of the continued fraction

We use the convention that K (empty set) = 1.

Type
Research Article
Copyright
Copyright © University College London 1977

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.Borosh, I.. “Rational continued fractions with small partial quotients”, Notices Amer. Math. Soc., 23 (1976), abstract 731–10–29, p. A-52.Google Scholar
2.Bumby, R. T.. “Dimensions of sets of continued fractions”, unpublished manuscript, 1975.Google Scholar
3.Good, I. J.. “The fractional dimension theory of continued fractions”, Proc. Cambridge Philos. Soc., 37 (1941), 199228.CrossRefGoogle Scholar
4.Motzkin, T. S. and Straus, E. G.. “Some combinatorial extremum problems”, Proc. Amer. Math. Soc., 7 (1956), 10141021.CrossRefGoogle Scholar