The fractional part of nθ+ø and Beatty sequences
Journal de Théorie des Nombres de Bordeaux, Tome 7 (1995) no. 2, pp. 387-406.
DOI : https://doi.org/10.5802/jtnb.148
Classification : 11B83
Mots clés: continued fraction, Beatty sequence
@article{JTNB_1995__7_2_387_0,
     author = {Komatsu, Takao},
     title = {The fractional part of $n\theta + \o $ and Beatty sequences},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {387--406},
     publisher = {Universit\'e Bordeaux I},
     volume = {7},
     number = {2},
     year = {1995},
     doi = {10.5802/jtnb.148},
     zbl = {0849.11027},
     mrnumber = {1378587},
     language = {en},
     url = {jtnb.centre-mersenne.org/item/JTNB_1995__7_2_387_0/}
}
Takao Komatsu. The fractional part of $n\theta + ø$ and Beatty sequences. Journal de Théorie des Nombres de Bordeaux, Tome 7 (1995) no. 2, pp. 387-406. doi : 10.5802/jtnb.148. https://jtnb.centre-mersenne.org/item/JTNB_1995__7_2_387_0/

[1] J.M. Borwein and P.B. Borwein, On the generating function of the integer part: [nα + γ], J. Number Theory 43 (1993), 293-318. | Zbl 0778.11039

[2] T.C. Brown, Descriptions of the characteristic sequence of an irrational, Canad. Math. Bull 36 (1993), 15-21. | MR 1205889 | Zbl 0804.11021

[3] L.V. Danilov, Some class of transcendental numbers, Mat. Zametki 12 (1972), 149-154= Math. Notes 12 (1972), 524-527. | MR 316391 | Zbl 0253.10026

[4] A.S. Fraenkel, M. Mushkin and U. Tassa, Determination of [nθ] by its sequence of differences, Canad. Math. Bull. 21 (1978), 441-446. | Zbl 0401.10018

[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. | MR 1091163 | Zbl 0721.11009

[6] T. Komatsu, A certain power series associated with Beatty sequences, manuscript.

[7] T. Komatsu, On the characteristic word of the inhomogeneous Beatty sequence, Bull. Austral. Math. Soc. 51 (1995), 337-351. | MR 1322798 | Zbl 0829.11012

[8] K. Nishioka, I. Shiokawa and J. Tamura, Arithmetical properties of certain power series, J. Number Theory 42 (1992), 61-87. | MR 1176421 | Zbl 0770.11039

[9] T. Van Ravenstein, The three gap theorem (Steinhaus conjecture), J. Austral. Math. Soc. (Series A) 45 (1988), 360-370. | MR 957201 | Zbl 0663.10039

[10] T. Van Ravenstein, G. Winley and K. Tognetti, Characteristics and the three gap theorem, Fibonacci Quarterly 28 (1990), 204-214. | MR 1064404 | Zbl 0709.11011

[11] K.B. Stolarsky, Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull. 19 (1976), 473-482. | MR 444558 | Zbl 0359.10028

[12] B.A. Venkov, Elementary Number Theory, Wolters-Noordhoff, Groningen, 1970. | MR 265267 | Zbl 0204.37101