On a relationship between the convergents of the nearest integer and regular continued fractions
Author:
William W. Adams
Journal:
Math. Comp. 33 (1979), 13211331
MSC:
Primary 10K10; Secondary 10K15
MathSciNet review:
537978
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Abstract: In this paper we derive a relation concerning the speed of convergence of the nearest integer and regular continued fractions. If , denote the convergents of the nearest integer and regular continued fractions of an irrational number , then for all n there is a such that . It is shown that for almost all . This problem is reduced to a special case of a general result concerning the frequency of partial quotients in the regular continued fraction (Theorem 2).
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DOI:
http://dx.doi.org/10.1090/S00255718197905379789
PII:
S 00255718(1979)05379789
Article copyright:
© Copyright 1979 American Mathematical Society
