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A theorem on approximation of irrational numbers by simple continued fractions

Published online by Cambridge University Press:  20 January 2009

Jingcheng Tong
Jingcheng Tong
Affiliation:
Department of Mathematical Sciences, University of North Florida, Jacksonville, FL 32216, U.S.A. Institute of Applied Mathematics, Academia Sinica, Peking, China
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Let ξ be an irrational number with simple continued fraction expansion ξ= [a0;a1,a2,…], Pn/qn be its nth convergent, . The following two theorems were proved by Müller [9] and rediscovered by Bagemihl and McLaughlin [1]:

Theorem 1.For n>1,

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 2 , June 1988 , pp. 197 - 204
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

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