Questions Around the Thue-Morse Sequence
References
- [1] AISTLEITNER, C.—HOFFER, R.—LARCHER, V.: On evil Kronecker sequences and lacunary trigonometric products, Ann. Inst. Fourier (Grenoble) 67 (2017), 637–687.
- [2] ALLOUCHE, J. P. —LIARDET, P.: Generalized Rudin-Shapiro sequences, Acta Arith. 60 (1991), 1–27.
- [3] BAI, Z. Q.: Multifractal analysis of the spectral measure of the Thue-Morse sequence: a periodic orbit approach, J. Phys. A: Math. Gen. 39 (2006), 1959–1973.
- [4] BUGEAUD, Y—CIPU, M.—MIGNOTTE, M.: On the representation of Fibonacci and Lucas numbers in an integer base, Ann. Math. Qu. 37 (2013), 31–43.
- [5] CASSELS, J.W.S.: On a problem of Steinhaus about normal numbers, Colloq. Math. 7 (1959), 95–101.
- [6] COQUET, J.: A summation formula related to the binary digits, Invent. Math. 73 (1983), 107–115.
- [7] DAVENPORT, H.: On certain exponential sums, J. Reine Angew. Math. 169 (1933), 158–176.
- [8] DAVENPORT, H.—ERDŐS, P.—LEVEQUE, W. J.: On Weyl’s criterion for uniform distribution, Michigan Math. J. 10 (1963), 311–314.
- [9] DARTYGE, C.—TENENBAUM, G.: Sommes des chiffres de multiples d’entiers, Ann. Inst. Fourier (Grenoble) 55 (2005), 2423–2474.
- [10] DOCHE, C.—HABSIEGER, L.: Moments of the Rudin-Shapiro polynomials, J. Fourier Anal. Appl. 10 (2004), 497–505.
- [11] DUMONT, J. M.: Discrépance des progressions arithmétiques dans la suite de Morse, C. R. Acad. Sci. Paris, SZ̆r. I 297 (1983), 145–148.
- [12] FALCONER, K.: Fractal geometry, mathematical foundations and applications, John Wiley & sons, 1990.
- [13] FOUVRY, E.—MAUDUIT, C.: Sommes des chiffres et nombres presque premiers, Math. Ann. 305 (1996), 571–599.
- [14] GELFOND, A. O.: Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arith. 13 (1968), 259–265.
- [15] GODRÈCHE, C.—LUCK, J.M.: Multifractal analysis in reciprocal space and the nature of the Fourier transform of self-similar structures. J. Phys. A 23 (1990), 3769–3797.
- [16] GRABNER, P. J.—LIARDET, P.—TICHY, R. F.: Spectral disjointness of dynamical systems related to some arithmetic functions. Publ. Math. Debrecen 66 (2005), 213–243.
- [17] HARE, K.—ROGINSKAYA, M.: A Fourier series formula for energy of measures with applications to Riesz products. Proc. Amer. Math. Soc. 131 (2003), 165–174.
- [18] HOST, B.: Nombres normaux, entropie, translations, Israel J. Math. 91 (1995), no. 1–3, 419–428.
- [19] KAMAE, T.: Cyclic extensions of odometer transformations and spectral disjointness, Israel J. Math. 59 (1987), 41–63.
- [20] KAMAE, T.: Number-theoretic problems involving two independent bases. In: Number theory and cryptography (Sydney, 1989), London Math. Soc. Lecture Note Ser., Vol. 154, Cambridge Univ. Press, Cambridge, 1990, pp. 196–203.
- [21] LIARDET, P.: Propriétés génériques de processus croisés. Israel J. Math. 39 (1981), 303–325.
- [22] MAUDUIT, C.: Multiplicative properties of the Thue-Morse sequence, Period. Math. Hungar. 43 (2001), 137–153.
- [23] MAUDUIT, C.—RIVAT, J.: Sur un problème de Gelfond: la somme des chiffres des nombres premiers, Ann. of Math.(2) 171 (2010), no. 3, 1591–1646.
- [24] MAUDUIT, C.—RIVAT, J.: La somme des chiffres des carrés, Acta Mathematica 203 (2009), 107–148.
- [25] NEWMAN, D. J.: On the number of binary digits in a multiple of three, Proc. Amer. Math. Soc. 21 (1969), 719–721.
- [26] PESIN, Y.: Dimension theory in dynamical systems, The university of Chicago Press, 1997.
- [27] PARREAU, F.—QUEFFÉLEC, M.: M0measures for the Walsh system, J. Fourier Anal. Appl. 15 (2009), 502–514.
- [28] QUEFFÉLEC, M.: Substitution dynamical systems–spectral analysis. (2nd edition.) In: Lecture Notes in Mathematics, Vol. 1294. Springer-Verlag, Berlin, 2010.
- [29] QUEFFÉLEC, M.: Une nouvelle propriété des suites de Rudin-Shapiro. Ann. Inst. Fourier (Grenoble) 37 (1987), 115–138.
- [30] RODGERS, B.: On the distribution of Rudin-Shapiro polynomials and lacunary walks on SU(2), Preprint. https://arxiv.org/pdf/1606.01637
- [31] SARNAK, P.: Spectra of singular measures as multipliers on Lp. J. Funct. Anal. 37 (1980), 302–317.
- [32] SARNAK, P.: Möbius randomness and dynamics, Not. S. Afr. Math. Soc. 43 (2012), 89–97.
- [33] SENGE, H. G.—STRAUS, E. G.: PV -numbers and sets of multiplicity, Period. Math. Hungar. 3 (1973), 93–100.
- [34] STEWART, C. L.: On the representation of an integer in two different bases, J. Reine Angew. Math. 319 (1980), 63–72.
- [35] TENENBAUM, G.: Sur la non dérivabilitédefonctions périodiques associées à certaines formules sommatoires In: The mathematics of Paul Erd˝os, I, Algorithms Combin. Vol. 13, Springer-Verlag, Berlin, 1997. pp. 117–128,
- [36] WEISS, B.: Almost no points on a Cantor set are very well approximable, R. Soc. Lond. Proc. Ser. A 457 (2001), no. 2008, 949–952.
- [37] WIENER, N.: Generalized harmonic analysis, Acta Math. 55 (1930), 117–258.
- [38] WOLFF, T. H.: Lectures on Harmonic Analysis, University Lecture Series, Vol. 29. AMS, Providence, RI, 2003.
- [39] YOUNG, L. S.: Dimension, entropy and Lyapunov exponents. Erg. Theory Dyn. Syst. 2 (1982), 109–124.
Language: English
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Submitted on: Jun 6, 2016
Accepted on: Mar 1, 2017
Published on: Jul 20, 2018
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