Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Continued fractions
with bounded partial quotients

Author: Pierre Stambul
Journal: Proc. Amer. Math. Soc. 128 (2000), 981-985
MSC (1991): Primary 11A55
Published electronically: August 5, 1999
MathSciNet review: 1662214
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper gives the exact bound of the continued fraction expansion of $\frac{a\theta+b}{c\theta+d}$ when $\theta$ has bounded partial quotients and $h\colon x\mapsto\frac{ax+b}{cx+d}$ is a Möbius transformation where all entries are integers.

References [Enhancements On Off] (What's this?)

  • [Cu-Me] T. W. Cusick and M. Mendès France, The Lagrange spectrum of a set, Acta Arith. 34 (1979), no. 4, 287–293. MR 543202,
  • [Ha] M. Hall, On the sum and product of continued fractions, Annals of Math. 48 (1947), 966-993. MR 9:226b
  • [La-Sh] J. C. Lagarias and J. O. Shallit, Linear Fractional Transformations of Continued Fractions with Bounded Partial Quotients, Journal de théorie des nombres de Bordeaux 9 (1997), 267-279. CMP 98:11
  • [Li-St] P. Liardet and P. Stambul, Algebraic Computations with Continued Fractions, Journal of Number Theory 73 (1998), 92-121. CMP 99:04
  • [Ra] George N. Raney, On continued fractions and finite automata, Math. Ann. 206 (1973), 265–283. MR 340166,
  • [Sh1] J. O. Shallit, Real numbers with bounded partial quotients: a survey, Enseign. Math. 38 (1992), 151-187.
  • [St1] P. Stambul, Contribution à l'étude des propriétés arithmétiques des fractions continuées, Thèse de l'Université de Provence (1994).

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11A55

Retrieve articles in all journals with MSC (1991): 11A55

Additional Information

Pierre Stambul
Affiliation: Centre de Mathématiques et Informatique, DSA, Université de Provence, 39, rue Joliot Curie, F-13543 Marseille Cedex 13, France

Keywords: Continued fractions, bounded partial quotients, M\"obius transformation, quadratic number, transducer.
Received by editor(s): June 5, 1998
Published electronically: August 5, 1999
Additional Notes: The author thanks P. Liardet who pointed out this problem
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2000 American Mathematical Society