The conjugate property for Diophantine approximation of continued fractions

Author:
Jing Cheng Tong

Journal:
Proc. Amer. Math. Soc. **105** (1989), 535-539

MSC:
Primary 11J04; Secondary 11J70, 11J72

DOI:
https://doi.org/10.1090/S0002-9939-1989-0937852-8

MathSciNet review:
937852

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an irrational number with simple continued fraction expansion , and be its th convergent. In this paper we first prove the duality of some inequalities, and then prove the following conjugate properties for symmetric and asymmetric Diophantine approximations.

(i) Among any three consecutive convergents , at least one satisfies

(ii) Let be a positive real number. Among any four consecutive convergents , at least one satisfies

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DOI:
https://doi.org/10.1090/S0002-9939-1989-0937852-8

Article copyright:
© Copyright 1989
American Mathematical Society