Modifications de nombres normaux par des transducteurs

Jean Marie Dumont; Alain Thomas

Acta Arithmetica (1994)

  • Volume: 68, Issue: 2, page 153-170
  • ISSN: 0065-1036

How to cite

top

Jean Marie Dumont, and Alain Thomas. "Modifications de nombres normaux par des transducteurs." Acta Arithmetica 68.2 (1994): 153-170. <http://eudml.org/doc/206652>.

@article{JeanMarieDumont1994,
author = {Jean Marie Dumont, Alain Thomas},
journal = {Acta Arithmetica},
keywords = {Champernowne number; transducers; normal numbers},
language = {fre},
number = {2},
pages = {153-170},
title = {Modifications de nombres normaux par des transducteurs},
url = {http://eudml.org/doc/206652},
volume = {68},
year = {1994},
}

TY - JOUR
AU - Jean Marie Dumont
AU - Alain Thomas
TI - Modifications de nombres normaux par des transducteurs
JO - Acta Arithmetica
PY - 1994
VL - 68
IS - 2
SP - 153
EP - 170
LA - fre
KW - Champernowne number; transducers; normal numbers
UR - http://eudml.org/doc/206652
ER -

References

top
  1. [BV] A. Bertrand-Mathis and B. Volkmann, On (ε,k)-normal words in connecting dynamical systems , Monatsh. Math. 107 (1989), 267-279. Zbl0648.10032
  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. Zbl0009.20002
  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. Zbl0776.11040
  4. [Ch] D. G. Champernowne, The construction of decimals normal in the scale of ten, J. London Math. Soc. 8 (1933), 254-260. Zbl0007.33701
  5. [CE] A. Copeland and P. Erdős, Note on normal numbers, Bull. Amer. Math. Soc. 52 (1946), 857-860. Zbl0063.00962
  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. Zbl0556.10036
  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. Zbl0713.11047
  14. [V] B. Volkmann, On modifying constructed normal numbers, Ann. Fac. Sci. Toulouse Math. (5) 1 (1979), 269-285. Zbl0429.10034

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.