Generalized Rudin-Shapiro sequences

Jean-Paul Allouche; Pierre Liardet

Acta Arithmetica (1991)

  • Volume: 60, Issue: 1, page 1-27
  • ISSN: 0065-1036

How to cite

top

Jean-Paul Allouche, and Pierre Liardet. "Generalized Rudin-Shapiro sequences." Acta Arithmetica 60.1 (1991): 1-27. <http://eudml.org/doc/206424>.

@article{Jean1991,
author = {Jean-Paul Allouche, Pierre Liardet},
journal = {Acta Arithmetica},
keywords = {Rudin-Shapiro sequence; 2-multiplicative sequences; number of words; binary expansions; Hadamard matrices; -multiplicative sequences; chain sequences; inequalities},
language = {eng},
number = {1},
pages = {1-27},
title = {Generalized Rudin-Shapiro sequences},
url = {http://eudml.org/doc/206424},
volume = {60},
year = {1991},
}

TY - JOUR
AU - Jean-Paul Allouche
AU - Pierre Liardet
TI - Generalized Rudin-Shapiro sequences
JO - Acta Arithmetica
PY - 1991
VL - 60
IS - 1
SP - 1
EP - 27
LA - eng
KW - Rudin-Shapiro sequence; 2-multiplicative sequences; number of words; binary expansions; Hadamard matrices; -multiplicative sequences; chain sequences; inequalities
UR - http://eudml.org/doc/206424
ER -

References

top
  1. [1] J.-P. Allouche, Les suites de Rudin-Shapiro généralisées: des suites déterministes de 'dimension' maximale, in: Colloque 'Fractals', C.I.R.M., Marseille 1986. 
  2. [2] J.-P. Allouche and M. Mendès France, On an extremal property of the Rudin-Shapiro sequence, Mathematika 32 (1985), 33-38. 
  3. [3] J.-P. Allouche and M. Mendès France, Suite de Rudin-Shapiro et modèle d'Ising, Bull. Soc. Math. France 113 (1985), 275-283. 
  4. [4] D. W. Boyd, J. Cook and P. Morton, On sequences of ±1's defined by binary patterns, Dissertationes Math. 283 (1989). Zbl0684.10011
  5. [5] J. Brillhart and L. Carlitz, Note on the Shapiro polynomials, Proc. Amer. Math. Soc. 25 (1970), 114-118. 
  6. [6] J. Brillhart, P. Erdős and P. Morton, On sums of Rudin-Shapiro coefficients II, Pacific J. Math. 107 (1978), 39-69. Zbl0469.10034
  7. [7] J. Brillhart und P. Morton, Über Summen von Rudin-Shapiroschen Koeffizienten, Illinois J. Math. 22 (1978), 126-148. 
  8. [8] G. Christol, T. Kamae, M. Mendès France et G. Rauzy, Suites algébriques, automates et substitutions, Bull. Soc. Math. France 108 (1980), 401-419. Zbl0472.10035
  9. [9] A. Cobham, Uniform tag-sequences, Math. Systems Theory 6 (1972), 164-192. Zbl0253.02029
  10. [10] J. Coquet and P. Liardet, A metric study involving independent sequences, J. Analyse Math. 49 (1987), 15-53. Zbl0645.10044
  11. [11] A. O. Gelfond, Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arith. 13 (1968), 259-265. Zbl0155.09003
  12. [12] J.-P. Kahane, Hélices et quasi-hélices, in: Math. Anal. Applic., Part B, Adv. in Math. Suppl. Stud. 7B, 1981, 417-433. 
  13. [13] L. Kuipers and H. Niederreiter, Uniform Distributions of Sequences, John Wiley & Sons, New York 1974. Zbl0281.10001
  14. [14] M. Lemańczyk, Toeplitz Z₂-extensions, Ann. Inst. H. Poincaré 24 (1) (1988), 1-43. 
  15. [15] P. Liardet, Propriétés harmoniques de la numération, d'après Jean Coquet, in: Colloque S.M.F.-C.N.R.S. 'Jean Coquet', Publications Mathématiques d'Orsay 88-02, Orsay 1988, 1-35. Zbl0713.11054
  16. [16] P. Liardet, Automata and generalized Rudin-Shapiro sequences, Arbeitsbericht, Math. Institut der Universität Salzburg, 1990. 
  17. [17] M. Mendès France et G. Tenenbaum, Dimension des courbes planes, papiers pliés et suite de Rudin-Shapiro, Bull. Soc. Math. France 109 (1981), 207-215. Zbl0468.10033
  18. [18] M. Queffélec, Une nouvelle propriété des suites de Rudin-Shapiro, Ann. Inst. Fourier (Grenoble) 37 (2) (1987), 115-138. Zbl0597.10054
  19. [19] M. Queffélec, Substitution Dynamical Systems-Spectral Analysis, Lecture Notes in Math. 1294, Springer, 1987. 
  20. [20] D. Rider, Transformations of Fourier coefficients, Pacific J. Math. 19 (1966), 347-355. Zbl0144.32001
  21. [21] W. Rudin, Some theorems on Fourier coefficients, Proc. Amer. Math. Soc. 10 (1959), 855-859. Zbl0091.05706
  22. [22] B. Saffari, Une fonction extrémale liée à la suite de Rudin-Shapiro, C. R. Acad. Sci. Paris 303 (1986), 97-100. Zbl0608.10051
  23. [23] A. Salem and A. Zygmund, Some properties of trigonometric series whose terms have random signs, Acta Math. 91 (1954), 245-301. Zbl0056.29001
  24. [24] H. S. Shapiro, Extremal problems for polynomials and power series, Thesis, M.I.T., 1951. 
  25. [25] A. P. Street, J. S. Wallis and W. D. Wallis, Combinatorics: Room Squares, Sum-free Sets, Hadamard Matrices, Lecture Notes in Math. 292, Springer, 1972. Zbl1317.05003

Citations in EuDML Documents

top
  1. Jean-Loup Mauclaire, A characterization of generalized Rudin-Shapiro sequences with values in a locally compact abelian group
  2. J.-P. Allouche, J. O. Shallit, Complexité des suites de Rudin-Shapiro généralisées
  3. Jean-Paul Allouche, Olivier Salon, Sous-suites polynomiales de certaines suites automatiques
  4. Fabien Durand, Dominique Schneider, Ergodic averages with deterministic weights
  5. Guy Barat, Valérie Berthé, Pierre Liardet, Jörg Thuswaldner, Dynamical directions in numeration

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.