The fractional part of n θ + ø and Beatty sequences

Takao Komatsu

Journal de théorie des nombres de Bordeaux (1995)

  • Volume: 7, Issue: 2, page 387-406
  • ISSN: 1246-7405

How to cite

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Komatsu, Takao. "The fractional part of $n\theta + ø$ and Beatty sequences." Journal de théorie des nombres de Bordeaux 7.2 (1995): 387-406. <http://eudml.org/doc/247659>.

@article{Komatsu1995,
author = {Komatsu, Takao},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {continued fraction; Beatty sequence; one-sided approximations; sorting problem; characteristic word},
language = {eng},
number = {2},
pages = {387-406},
publisher = {Université Bordeaux I},
title = {The fractional part of $n\theta + ø$ and Beatty sequences},
url = {http://eudml.org/doc/247659},
volume = {7},
year = {1995},
}

TY - JOUR
AU - Komatsu, Takao
TI - The fractional part of $n\theta + ø$ and Beatty sequences
JO - Journal de théorie des nombres de Bordeaux
PY - 1995
PB - Université Bordeaux I
VL - 7
IS - 2
SP - 387
EP - 406
LA - eng
KW - continued fraction; Beatty sequence; one-sided approximations; sorting problem; characteristic word
UR - http://eudml.org/doc/247659
ER -

References

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  1. [1] J.M. Borwein and P.B. Borwein, On the generating function of the integer part: [nα + γ], J. Number Theory43 (1993), 293-318. Zbl0778.11039
  2. [2] T.C. Brown, Descriptions of the characteristic sequence of an irrational, Canad. Math. Bull36 (1993), 15-21. Zbl0804.11021MR1205889
  3. [3] L.V. Danilov, Some class of transcendental numbers, Mat. Zametki12 (1972), 149-154= Math. Notes12 (1972), 524-527. Zbl0253.10026MR316391
  4. [4] A.S. Fraenkel, M. Mushkin and U. Tassa, Determination of [nθ] by its sequence of differences, Canad. Math. Bull.21 (1978), 441-446. Zbl0401.10018
  5. [5] Sh. Ito and S. Yasutomi, On continued fractions, substitutions and characteristic sequences [nx + y] - [(n - 1)x + y], Japan. J. Math.16 (1990), 287-306. Zbl0721.11009MR1091163
  6. [6] T. Komatsu, A certain power series associated with Beatty sequences, manuscript. Zbl0858.11013
  7. [7] T. Komatsu, On the characteristic word of the inhomogeneous Beatty sequence, Bull. Austral. Math. Soc.51 (1995), 337-351. Zbl0829.11012MR1322798
  8. [8] K. Nishioka, I. Shiokawa and J. Tamura, Arithmetical properties of certain power series, J. Number Theory42 (1992), 61-87. Zbl0770.11039MR1176421
  9. [9] T. Van Ravenstein, The three gap theorem (Steinhaus conjecture), J. Austral. Math. Soc. (Series A) 45 (1988), 360-370. Zbl0663.10039MR957201
  10. [10] T. Van Ravenstein, G. Winley and K. Tognetti, Characteristics and the three gap theorem, Fibonacci Quarterly28 (1990), 204-214. Zbl0709.11011MR1064404
  11. [11] K.B. Stolarsky, Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull.19 (1976), 473-482. Zbl0359.10028MR444558
  12. [12] B.A. Venkov, Elementary Number Theory, Wolters-Noordhoff, Groningen, 1970. Zbl0204.37101MR265267

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