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Denominator Sequences of continued fractions I

Published online by Cambridge University Press:  09 April 2009

R. T. Worley
R. T. Worley
Affiliation:
Monash University Clayton, Vic. 3168, Australia
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Let α be an irrational number with simple continued fraction α = (a0, a1, a2,…). The problem studied is that of whether the sequence (qn) of denominators of the convergents pn/qn to α has a subsequence (Bn) = (qin} which is the sequence of denominators of convergents An/Bn to a different number α′. In other words, does there exist a subsequence {qin} which satisfies qio= 1 and For example, the sequence of denominators of convergents to ½(3 − e) is a subsequence of the sequence of denominators of convergents to ε.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 1 , February 1973 , pp. 112 - 116
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Schmidt, W. M., ‘On simultaneous approximations of two algebraic numbers by rationals’ Acta Math. 119 (1967), 27–50.Google Scholar