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The spectrum of one-dimensional quasilattices. (English. Russian original) Zbl 1209.11071
Sib. Math. J. 51, No. 1, 53-56 (2010); translation from Sib. Mat. Zh. 51, No. 1, 68-73 (2010).
The author proves theorems on the spectrum of the one-dimensional quasilattices resulting from irrational rotations of the circle.

MSC:
11K31 Special sequences
11K36 Well-distributed sequences and other variations
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[1] Weyl H., ”Uniform distribution modulo 1,” in: H. Weyl, Selected Works [Russian translation], Nauka, Moscow, 1984, pp. 58–93.
[2] Korobov N. M., Trigonometric Series and Some of Its Applications [in Russian], Nauka, Moscow (1989). · Zbl 0665.10026
[3] Karatsuba A. A., ”Fractional parts of functions of a special form,” Izv.: Math., 59, No. 4, 721–740 (1995). · Zbl 0874.11050 · doi:10.1070/IM1995v059n04ABEH000031
[4] Karatsuba A. A., ”On fractional parts of rapidly growing functions,” Izv.: Math., 65, No. 4, 727–748 (2001). · Zbl 1028.11045 · doi:10.1070/IM2001v065n04ABEH000349
[5] Karatsuba A. A., Arkhipov G. I., and Chubarikov V. N., ”Distribution of fractional parts of polynomials in several variables,” Math. Notes, 25, No. 1, 3–9 (1979). · Zbl 0416.10038
[6] Kuipers L. and Niderreiter G., Uniform Distribution of Sequences, Wiley and Sons, New York (1974).
[7] Drmota M. and Tichy R. F., Sequences, Discrepancies and Applications, Springer-Verlag, Berlin (1997). · Zbl 0877.11043
[8] Arnoux P., Berthe V., Ei H., and Ito S., ”Tilings, quasicrystals, discrete planes, generalized substitutions and multidimensional continued fractions,” in: Discrete Models: Combinatorics, Computation and Geometry, Paris, 2001, pp. 59–78. · Zbl 1017.68147
[9] Zhuravlev V. G., One-Dimensional Fibonacci Tilings and Derivatives of Two-Colour Rotations of a Circle [Preprint / Max-Plank-Institut für Mathematik; No. 59], Leipzig (2004).
[10] Arnol’d V. I., ”Remarks on quasicrystallic symmetry,” in: F. Klein, Lectures on the Icosahedron and the Solution of the Fifth Degree [Russian translation], Nauka, Moscow, 1989, pp. 291–300.
[11] De Bruijn N. G., ”Sequences of zeros and ones generated by special production rules,” Kon. Nederl. Acad. Wetensch. Proc. Ser. A, 84, 38–52 (1982).
[12] Moody R. V., ”Model sets: a survey,” in: Quasicrystals to More Complex Systems, Les Houches, 1998 (F. Alex and J.-P. Gazeau, eds.), Centre de Physique des Houches, Springer-Verlag, Berlin, 2000, 13, pp. 145–166.
[13] Fogg N. P., Substitutions in Dynamics, Arithmetics and Combinatorics, Springer-Verlag, Berlin and Heidelberg (2002). · Zbl 1014.11015
[14] Zhuravlev V. G., ”Even Fibonacci numbers: the binary additive problem, the distribution over progressions, and the spectrum,” St. Petersburg Math. J., 20, No. 3, 339–360 (2009). · Zbl 1206.11020 · doi:10.1090/S1061-0022-09-01051-6
[15] Krasil’shchikov V. V. and Shutov A. V., ”On the distribution of sequences by a variable modulus,” in: Proceedings of the XXVIII Conference of Young Scientists of the Department of Mechanics and Mathematics, Moscow Univ., Moscow, 2006, pp. 90–93.
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