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1999 | 91 | 4 | 329-349
Tytuł artykułu

Harmonic properties of the sum-of-digits function for complex bases

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
91
Numer
4
Strony
329-349
Opis fizyczny
Daty
wydano
1999
otrzymano
1998-06-19
poprawiono
1999-04-16
Twórcy
  • Institut für Mathematik A, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria
  • Université de Provence CMI, Château Gombert, 39, rue Joliot-Curie, 13453 Marseille, Cedex 13, France
Bibliografia
  • [1] W. Ambrose, Spectral resolution of groups of unitary operators, Duke Math. J. 11 (1944), 589-595.
  • [2] J.-P. Conze, Equirépartition et ergodicité de transformations cylindriques, Séminaire de Probabilité, Université de Rennes, 1976.
  • [3] J. Coquet, Power sums of digital sums, J. Number Theory 22 (1986), 161-176.
  • [4] J. Coquet and P. van den Bosch, A summation formula involving Fibonacci digits, ibid. 22 (1986), 139-146.
  • [5] H. Delange, Sur la fonction sommatoire de la fonction ``somme des chiffres'', Enseign. Math. (2) 21 (1975), 31-47.
  • [6] M. P. Drazin and J. S. Griffith, On the decimal representation of integers, Proc. Cambridge Philos. Soc. 48 (1952), 555-565.
  • [7] M. Drmota and R. F. Tichy, Sequences, Discrepancies and Applications, Lecture Notes in Math. 1651, Springer, 1997.
  • [8] S. Eilenberg, Automata, Languages and Machines, Vol. A, Academic Press, 1974.
  • [9] N. J. Fine, The distribution of the sum of digits (mod p), Bull. Amer. Math. Soc. 71 (1965), 651-652.
  • [10] P. Flajolet, P. J. Grabner, P. Kirschenhofer, ßs H. Prodinger and R. F. Tichy, Mellin transforms and asymptotics: digital sums, Theoret. Comput. Sci. 123 (1994), 291-314.
  • [11] H. Furstenberg, Ergodic behaviour of the diagonal measures and the theorem of Szemeredi on arithmetic progressions, J. Anal. Math. 34 (1978), 275-291.
  • [12] A. O. Gelfond, Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arith. 13 (1968), 259-266.
  • [13] P. J. Grabner, ßs P. Kirschenhofer and H. Prodinger, The sum-of-digits function for complex bases, J. London Math. Soc. 57 (1998), 20-40.
  • [14] P. J. Grabner, ßs P. Liardet and R. F. Tichy, Odometers and systems of numeration, Acta Arith. 70 (1995), 103-123.
  • [15] P. J. Grabner and R. F. Tichy, α-expansions, linear recurrences, and the sum-of-digits function, Manuscripta Math. 70 (1991), 311-324.
  • [16] H. Helson, Cocycles on the circle, J. Operator Theory 16 (1986), 189-199.
  • [17] E. Hewitt and K. A. Ross, Abstract Harmonic Analysis, Vol. 1, Springer, Berlin, 1963.
  • [18] H. Hida, Elementary Theory of L-Functions and Eisenstein Series, Cambridge Univ. Press, 1993.
  • [19] E. Hlawka, ßs J. Schoissengeier and R. Taschner, Geometric and Analytic Theory of Numbers, Springer, 1991.
  • [20] T. Kamae, Mutual singularity of spectra of dynamical systems given by the 'sum of digits' to different bases, Astérisque 49 (1977), 109-114.
  • [21] I. Kátai and B. Kovács, Kanonische Zahlsysteme in der Theorie der quadratischen algebraischen Zahlen, Acta Sci. Math. (Szeged) 42 (1980), 99-107.
  • [22] I. Kátai and B. Kovács, Canonical number systems in imaginary quadratic fields, Acta Math. Acad. Sci. Hungar. 37 (1981), 159-164.
  • [23] I. Kátai and J. Szabó, Canonical number systems for complex integers, Acta Sci. Math. (Szeged) 37 (1975), 255-260.
  • [24] A. B. Katok and A. M. Stepin, Approximations in ergodic theory, Uspekhi Mat. Nauk 22 (1967), no. 5, 81-106.
  • [25] D. E. Knuth, The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, Addison Wesley, London, 1981.
  • [26] B. Kovács, Canonical number systems in algebraic number fields, Acta Math. Acad. Sci. Hungar. 37 (1981), 405-407.
  • [27] B. Kovács and A. Pethő, Number systems in integral domains, especially in orders of algebraic number fields, Acta Sci. Math. (Szeged) 55 (1991), 287-299.
  • [28] U. Krengel, Ergodic Theorems, de Gruyter, 1985.
  • [29] L. Kuipers and H. Niederreiter, Uniform Distribution of Sequences, Wiley, 1974.
  • [30] P. Liardet, Répartition et ergodicité, Séminaire de Théorie des Nombres Delange-Pisot-Poitou, 19e année, Paris, 1977/78, 12 pp.
  • [31] P. Liardet, Propriétés harmoniques de la numération suivant Jean Coquet, in: Colloque de Théorie Analytique des Nombres 'Jean Coquet', Publ. Math. Orsay 88-02, 1-35, CIRM, 1985.
  • [32] W. Narkiewicz, Elementary and Analytic Theory of Algebraic Numbers, Springer, Berlin, 1990.
  • [33] W. Parry, Compact abelian group extensions of discrete dynamical systems, Z. Wahrsch. Verw. Gebiete 13 (1969), 95-113.
  • [34] M. Queffélec, Mesures spectrales associées à certaines suites arithmétiques, Bull. Soc. Math. France 107 (1979), 385-421.
  • [35] K. Schmidt, Lectures on Cocycles and Ergodic Transformation Groups, McMillan, Delhi, 1977.
  • [36] G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory, Cambridge Stud. Adv. Math. 46, Cambridge Univ. Press, 1995.
  • [37] J. M. Thuswaldner, The sum of digits function in number fields, Bull. London Math. Soc. 30 (1998), 37-45.
  • [38] J. R. Trollope, An explicit expression for binary digital sums, Math. Mag. 41 (1968), 21-27.
  • [39] R. J. Zimmer, Extension of ergodic group actions, Illinois J. Math. 20 (1976), 373-409.
Typ dokumentu
Bibliografia
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