• Medientyp: E-Artikel
  • Titel: Good Approximations and Continued Fractions
  • Beteiligte: Kraaikamp, Cor; Liardet, Pierre
  • Erschienen: American Mathematical Society, 1991
  • Erschienen in: Proceedings of the American Mathematical Society, 112 (1991) 2, Seite 303-309
  • Sprache: Englisch
  • ISSN: 0002-9939; 1088-6826
  • Entstehung:
  • Anmerkungen:
  • Beschreibung: <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>
  • Zugangsstatus: Freier Zugang