Download PDF - Modifications de nombres normaux par des transducteursAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Modifications de nombres normaux par des transducteurs

Authors 1, 2

Affiliations

  1. Laboratoire, de Mathématiques Discrètes, U.P.R. 9016, Case 930, 163, avenue de Luminy, F-13288 Marseille Cedex 9, France
  2. UFR-MIM, Faculté des Sciences de St Charles, Université de Provence, case F, 3, place Victor Hugo, F-13331 Marseille Cedex 3, France

Bibliography

  1. [BV] A. Bertrand-Mathis and B. Volkmann, On (ε,k)-normal words in connecting dynamical systems , Monatsh. Math. 107 (1989), 267-279.
  2. [Be] A. S. Besicovitch, The asymptotic distribution of the numerals in the decimal representation of the squares of the natural numbers, Math. Z. 39 (1935), 146-156.
  3. [BlDT] F. Blanchard, J. M. Dumont and A. Thomas, Generic sequences, transducers and multiplication of normal numbers, Israel J. Math. 80 (1992), 257-287.
  4. [Ch] D. G. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc. 8 (1933), 254-260.
  5. [CE] A. Copeland and P. Erdős, Note on normal numbers, Bull. Amer. Math. Soc. 52 (1946), 857-860.
  6. [DT] J. M. Dumont et A. Thomas, Une modification multiplicative des nombres g-normaux, Ann. Fac. Sci. Toulouse Math. (5) 8 (1986/87), 367-376.
  7. [G] P. Grabner, On digit expansions with respect to second order linear recurring sequences, in: Number Theoretic Analysis (Vienna, 1988-89), Lecture Notes in Math. 1452, Springer, Berlin, 1990, 58-64.
  8. [NS1] Y.-N. Nakaï and I. Shiokawa, A class of normal numbers, Japan J. Math. 16 (1990), 17-29.
  9. [NS2] Y.-N. Nakaï and I. Shiokawa, A class of normal numbers. II, in: Number Theory and Cryptography (Sydney, 1989), J. H. Loxton (ed.), London Math. Soc. Lecture Note Ser. 154, Cambridge Univ. Press, Cambridge, 1990, 204-210.
  10. [NS3] Y.-N. Nakaï and I. Shiokawa, Discrepancy estimates for a class of normal numbers, Acta Arith. 62 (1992), 271-284.
  11. [Re] A. Rényi, Calcul des probabilités, Collect. Univ. Math. 21, Dunod, Paris, 1966.
  12. [Sc] J. Schiffer, Discrepancy of normal numbers, Acta Arith. 47 (1986), 175-186.
  13. [SV] P. Szüsz and B. Volkmann, Sur des nombres normaux définis par un polynôme, Séminaire de théorie des nombres, 1987-1988 (Talence, 1987-1988), Exp. No. 42, 4pp., Univ. Bordeaux I, Talence.
  14. [V] B. Volkmann, On modifying constructed normal numbers, Ann. Fac. Sci. Toulouse Math. (5) 1 (1979), 269-285.
Acta Arithmetica
1994/68/2
Export to PBN, Opens in new tab
Pages:
153-170
Main language of publication
French
Received
1993-10-26
Accepted
1994-03-10
Published
1994
Exact and natural sciences