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Continued fractions with bounded partial quotients

Author(s): Pierre Stambul
Journal: Proc. Amer. Math. Soc. 128 (2000), 981-985.
MSC (1991): Primary 11A55
Posted: August 5, 1999
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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:

[Cu-Me]
T. W. Cusick and M. Mendès France, The Lagrange spectrum of a set, Acta Arith. 34 (1979), 287-293. MR 80i:10038a

[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]
G. N. Raney, On continued fractions and finite automata, Math. Annalen 206 (1973), 265-283. MR 49:4922

[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).

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Additional Information:

Pierre Stambul
Affiliation: Centre de Mathématiques et Informatique, DSA, Université de Provence, 39, rue Joliot Curie, F-13543 Marseille Cedex 13, France
Email: stambul.pierre@wanadoo.fr

DOI: 10.1090/S0002-9939-99-05312-5
PII: S 0002-9939(99)05312-5
Keywords: Continued fractions, bounded partial quotients, M\"obius transformation, quadratic number, transducer.
Received by editor(s): June 5, 1998
Posted: August 5, 1999
Additional Notes: The author thanks P. Liardet who pointed out this problem
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2000, American Mathematical Society

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