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Media type:
E-Article
Title:
Good Approximations and Continued Fractions
Contributor:
Kraaikamp, Cor;
Liardet, Pierre
imprint:
American Mathematical Society, 1991
Published in:Proceedings of the American Mathematical Society
Language:
English
ISSN:
0002-9939;
1088-6826
Origination:
Footnote:
Description:
<p>Let (q<sub>n</sub>)<sub>n</sub>be the sequence of best approximation denominators of an irrational number α. The set of real numbers x for which q<sub>nx</sub>→ 0 (mod 1) is studied. It is shown that a number x belongs to αZ (mod 1) if and only if a simple condition on the speed of the convergence related to an arithmetic property of α is satisfied. This set is uncountable whenever α has unbounded partial quotients.</p>