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Almost everywhere exponential convergence of the modified Jacobi—Perron algorithm

Published online by Cambridge University Press:  19 September 2008

S. Ito
Affiliation:
Department of Mathematics, Tsuda College, Tsuda-machi, Kodaira, Tokyo, Japan
M. Keane
Affiliation:
Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
M. Ohtsuki
Affiliation:
Department of Mathematics, Tsuda College, Tsuda-machi, Kodaira, Tokyo, Japan

Abstract

We prove that there exists a constant δ > 0 such that for almost every pair of numbers α and β there exists n0= n0(α,β) such that for any nn0

where the integers pn,qn, rn are provided by the modified Jacobi-Perron algorithm.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1993

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References

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Almost everywhere exponential convergence of the modified Jacobi—Perron algorithm
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