Approximation by continued fractions-Reference-Cited by-同舟云学术

Approximation by continued fractions

Published:1974 Issue:3 Volume:45 Page:323-324
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Nathanson Melvyn B.

Abstract

Let x x be a real irrational number whose continued fraction has infinitely many partial quotients not less than k k . A simple proof is given that the inequality | x − p / q | > ( k 2 + 4 ) − 1 / 2 q − 2 |x - p/q| > (k^2 + 4)^{-1/2} q^{-2} has infinitely many rational solutions p / q p/q . The constant ( k 2 + 4 ) − 1 / 2 (k^2 + 4)^{-1/2} is best possible.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-045-03/S0002-9939-1974-0349594-X/S0002-9939-1974-0349594-X.pdf

Reference2 articles.

1. Hurwitz’ theorem;Cohn, J. H. E.;Proc. Amer. Math. Soc.,1973

2. G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Oxford Univ. Press, London, 1960.

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On a theorem of Borel on diophantine approximation;The Ramanujan Journal;2024-08-07

2. Second basic theorem of Hurwitz*;Lithuanian Mathematical Journal;2016-01

3. Sharpening of theorems of Vahlen and Hurwitz and approximation properties of the golden ratio;Archiv der Mathematik;2015-07-18

4. A theorem on approximation of irrational numbers by simple continued fractions;Proceedings of the Edinburgh Mathematical Society;1988-06

5. The conjugate property of the Borel theorem on diophantine approximation;Mathematische Zeitschrift;1983-06