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}, mrnumber = {1378587}, zbl = {0849.11027}, language = {en}, url = {http://www.numdam.org/item/JTNB_1995__7_2_387_0/} }
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 SP - 387 EP - 406 VL - 7 IS - 2 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1995__7_2_387_0/ LA - en ID - JTNB_1995__7_2_387_0 ER -
Komatsu, Takao. 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. http://www.numdam.org/item/JTNB_1995__7_2_387_0/
[1] On the generating function of the integer part: [nα + γ], J. Number Theory 43 (1993), 293-318. | Zbl
and ,[2] Descriptions of the characteristic sequence of an irrational, Canad. Math. Bull 36 (1993), 15-21. | MR | Zbl
,[3] Some class of transcendental numbers, Mat. Zametki 12 (1972), 149-154= Math. Notes 12 (1972), 524-527. | MR | Zbl
,[4] Determination of [nθ] by its sequence of differences, Canad. Math. Bull. 21 (1978), 441-446. | Zbl
, and ,[5] On continued fractions, substitutions and characteristic sequences [nx + y] - [(n - 1)x + y], Japan. J. Math. 16 (1990), 287-306. | MR | Zbl
and ,[6] A certain power series associated with Beatty sequences, manuscript.
,[7] On the characteristic word of the inhomogeneous Beatty sequence, Bull. Austral. Math. Soc. 51 (1995), 337-351. | MR | Zbl
,[8] Arithmetical properties of certain power series, J. Number Theory 42 (1992), 61-87. | MR | Zbl
, and ,[9] The three gap theorem (Steinhaus conjecture), J. Austral. Math. Soc. (Series A) 45 (1988), 360-370. | MR | Zbl
,[10] Characteristics and the three gap theorem, Fibonacci Quarterly 28 (1990), 204-214. | MR | Zbl
, and ,[11] Beatty sequences, continued fractions, and certain shift operators, Canad. Math. Bull. 19 (1976), 473-482. | MR | Zbl
,[12] Elementary Number Theory, Wolters-Noordhoff, Groningen, 1970. | MR | Zbl
,