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Propriétés ergodiques des suites q -multiplicatives

Emmanuel Lesigne; Christian Mauduit

Compositio Mathematica (1996)

  • Volume: 100, Issue: 2, page 131-169
  • ISSN: 0010-437X

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Lesigne, Emmanuel, and Mauduit, Christian. "Propriétés ergodiques des suites $q$-multiplicatives." Compositio Mathematica 100.2 (1996): 131-169. <http://eudml.org/doc/90425>.

@article{Lesigne1996,
author = {Lesigne, Emmanuel, Mauduit, Christian},
journal = {Compositio Mathematica},
keywords = {Besicovitch almost periodic sequences; uniform convergence of exponential sums; strictly ergodic -multiplicative sequences; good sequences},
language = {fre},
number = {2},
pages = {131-169},
publisher = {Kluwer Academic Publishers},
title = {Propriétés ergodiques des suites $q$-multiplicatives},
url = {http://eudml.org/doc/90425},
volume = {100},
year = {1996},
}

TY - JOUR
AU - Lesigne, Emmanuel
AU - Mauduit, Christian
TI - Propriétés ergodiques des suites $q$-multiplicatives
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 100
IS - 2
SP - 131
EP - 169
LA - fre
KW - Besicovitch almost periodic sequences; uniform convergence of exponential sums; strictly ergodic -multiplicative sequences; good sequences
UR - http://eudml.org/doc/90425
ER -

References

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  1. [B-S] Bellman, R. et Shapiro, H.N.: A problem in additive number theory, Ann. of Math., 49 (1948), 333-340. Zbl0031.25401MR23864
  2. [B-L] Bellow, A. et Losert, V.: The weighted pointwise ergodic theorem and the individual ergodic theorem along subsequences, Trans. Am. Math. Soc., 288 (1985), 307-345. Zbl0619.47004MR773063
  3. [Bes] Besineau, J.: Indépendance statistique d'ensembles liés à la somme des chiffres, Acta Arithm., 20 (1972), 401-416. Zbl0252.10052MR304335
  4. [Coq] Coquet, J.: Contribution à l'étude harmonique des suites arithmétiques, Thèse d'Etat, Orsay (1978). Zbl0462.10040
  5. [C-K-M] Coquet, J., Kamae, T. et Mendès-France M.: Sur la mesure spectrale de certains suites arithmétiques, Bull. Soc. Math. France, 105 (1977), 369-384. Zbl0383.10035MR472749
  6. [Del] Delange, H.: Sur les fonctions q-additives ou q-multiplicatives, Acta Arithm., 21(1972), 285-298. Zbl0219.10062MR309891
  7. [Gue] Guelfond, A.O.: Sur les nombres qui ont des propriétés additives et multiplicatives données, Acta Arithm., 13 (1968), 259-265. Zbl0155.09003MR220693
  8. [Kea] Keane, M.: Generalized Morse Sequences, Z. Wahrscheinlichkeitstheorie verw. Geb., 10 (1968), 335-353. Zbl0162.07201MR239047
  9. [Kre] Krengel, U.: Ergodic Theorems. De Gruyter Studies in Mathematics6 (1985). Zbl0575.28009MR797411
  10. [L-M-M] Lesigne, E., Mauduit, C. et Mossé, B.: Le théorème ergodique le long d'une suite q-multiplicative, Compositio Mathematica, 93 (1994), 49-79. Zbl0818.28006MR1286798
  11. [Lia 1] Liardet, P.: Regularities of distribution, Compositio Mathematica, 61 (1987), 267-293. Zbl0619.10053MR883484
  12. [Lia 2] Liardet, P.: Propriétés harmoniques de la numération, suivant Jean Coquet; Colloque de Théorie Analytique des Nombres J. Coquet, Publications Mathématiques d'Orsay, Orsay (1988). Zbl0713.11054MR952862
  13. [Mar] Martin, J.C.: Generalized Morse sequences on n symbols, Proc. Am. Math. Soc.54 (1976), 379-383. Zbl0317.54054MR391058
  14. [Mos] Mossé, B.: q-adic spectral analysis of some arithmetic sequences, Theoritical Computer Science65 (1989), 249-263. Zbl0679.10044MR1020491
  15. [Que] Queffélec, M.: Mesures spectrales associées à certaines suites arithmétiques, Bull. Soc. Math. France.107 (1979), 385-421. Zbl0435.42007MR557078
  16. [Rau] Rauzy, G.: Propriétés statistiques de suites arithmétiques. Collection SUP, Presses Universitaires de France, Paris (1976). Zbl0337.10036MR409397

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