Sur la mesure spectrale des suites multiplicatives

Jean Coquet

Annales de l'institut Fourier (1979)

  • Volume: 29, Issue: 3, page 163-170
  • ISSN: 0373-0956

Abstract

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It is proved that, if a multiplicative sequence, the modulus of which is ≤ 1 , has non-empty Fourier-Bohr spectrum, its spectral measure is pure point. The proof, based on a result of J-.P. Bertrandias, avoids the calculation of the covariance.

How to cite

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Coquet, Jean. "Sur la mesure spectrale des suites multiplicatives." Annales de l'institut Fourier 29.3 (1979): 163-170. <http://eudml.org/doc/74416>.

@article{Coquet1979,
abstract = {Dans cet article, nous démontrons que la mesure spectrale d’une suite multiplicative de module $\le 1$ dont le spectre de Fourier-Bohr est non vide, est atomique. La preuve, basée sur un résultat de J.-P. Bertrandias, évite le calcul de la corrélation.},
author = {Coquet, Jean},
journal = {Annales de l'institut Fourier},
keywords = {arithmetic function; spectral measure; multiplicative sequence},
language = {fre},
number = {3},
pages = {163-170},
publisher = {Association des Annales de l'Institut Fourier},
title = {Sur la mesure spectrale des suites multiplicatives},
url = {http://eudml.org/doc/74416},
volume = {29},
year = {1979},
}

TY - JOUR
AU - Coquet, Jean
TI - Sur la mesure spectrale des suites multiplicatives
JO - Annales de l'institut Fourier
PY - 1979
PB - Association des Annales de l'Institut Fourier
VL - 29
IS - 3
SP - 163
EP - 170
AB - Dans cet article, nous démontrons que la mesure spectrale d’une suite multiplicative de module $\le 1$ dont le spectre de Fourier-Bohr est non vide, est atomique. La preuve, basée sur un résultat de J.-P. Bertrandias, évite le calcul de la corrélation.
LA - fre
KW - arithmetic function; spectral measure; multiplicative sequence
UR - http://eudml.org/doc/74416
ER -

References

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  1. [1] J.P. BERTRANDIAS, Espaces de fonctions bornées et continues en moyenne asymptotique d'ordre p, Bull. Soc. Math. France, mémoire 5 (1966), 1-106. Zbl0148.11701MR33 #4598
  2. [2] J. COQUET, T. KAMAE, M. MENDES-FRANCE, Sur la mesure spectrale de certaines suites arithmétiques, Bull. Soc. Math. France, 105 (1977), 369-384. Zbl0383.10035MR57 #12439
  3. [3] J. COQUET, Sur les fonctions q-multiplicatives pseudo-aléatoires, C.R.A.S., Paris, 282 (1976), 175-178. Zbl0316.10032MR53 #5518
  4. [4] H. DABOUSSI, H. DELANGE, Quelques propriétés des fonctions multiplicatives de module ≤1, C.R.A.S., Paris, 278 (1974), 657-660. Zbl0292.10034MR48 #11028
  5. [5] H. DABOUSSI, M. MENDES-FRANCE, Spectrum, almost-periodicity and equidistribution modulo 1, Studia Scientiarum Math. Hung., 9 (1974), 173-180. Zbl0321.10043
  6. [6] G. HALASZ, Uber die Mittelwerte multiplikativer zahlentheoretischer Funktionen, Acta Math. Acad. Sc. Hungaricae, 19 (1968), 365-403. Zbl0165.05804MR37 #6254
  7. [7] J. KUBILIUS, Probabilistic methods in the theory of numbers, A.M.S., Mathematical monographs, 11. Zbl0133.30203MR28 #3956

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