On the distribution of the values of an additive arithmetical function with values in a locally compact abelian group

Jean-Loup Mauclaire

Acta Arithmetica (1994)

  • Volume: 68, Issue: 3, page 201-212
  • ISSN: 0065-1036

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Jean-Loup Mauclaire. "On the distribution of the values of an additive arithmetical function with values in a locally compact abelian group." Acta Arithmetica 68.3 (1994): 201-212. <http://eudml.org/doc/206655>.

@article{Jean1994,
author = {Jean-Loup Mauclaire},
journal = {Acta Arithmetica},
keywords = {additive functions; limiting distribution; locally compact commutative groups},
language = {eng},
number = {3},
pages = {201-212},
title = {On the distribution of the values of an additive arithmetical function with values in a locally compact abelian group},
url = {http://eudml.org/doc/206655},
volume = {68},
year = {1994},
}

TY - JOUR
AU - Jean-Loup Mauclaire
TI - On the distribution of the values of an additive arithmetical function with values in a locally compact abelian group
JO - Acta Arithmetica
PY - 1994
VL - 68
IS - 3
SP - 201
EP - 212
LA - eng
KW - additive functions; limiting distribution; locally compact commutative groups
UR - http://eudml.org/doc/206655
ER -

References

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  1. [1] N. Bourbaki, Eléments de mathématique. Intégration, chap. I-IV, 2ème éd., Hermann, Paris, 1965. 
  2. [2] H. Delange, On the distribution modulo 1 of additive functions, J. Indian Math. Soc. 34 (1970), 215-235. Zbl0234.10044
  3. [3] P. D. T. A. Elliott, Probabilistic Number Theory I, Grundlehren Math. Wiss. 239, Springer, New York, 1979. 
  4. [4] P. D. T. A. Elliott, Arithmetic Functions and Integer Products, Grundlehren Math. Wiss. 272, Springer, New York, 1985. Zbl0559.10032
  5. [5] P. D. T. A. Elliott, On the limiting distribution of additive functions (mod 1), Pacific J. Math. 38 (1971), 49-59. Zbl0228.10029
  6. [6] P. D. T. A. Elliott and C. Ryavec, The distribution of values of additive arithmetical functions, Acta Math. 126 (1971), 143-164. Zbl0221.10056
  7. [7] P. Hartman, Infinite convolutions on locally compact abelian groups and additive functions, Trans. Amer. Math. Soc. 214 (1975), 215-231. Zbl0355.60006
  8. [8] B. V. Levine and N. M. Timofeev, On the distribution of values of additive functions, Acta Arith. 26 (1975), 333-364. Zbl0318.10041
  9. [9] E. Manstavicius, The distribution of additive arithmetic functions modulo 1, Litovsk. Mat. Sb. 13 (1973), 101-108. Zbl0264.10042
  10. [10] J. L. Mauclaire, Distribution des valeurs d'une fonction arithmétique additive à valeurs dans un groupe abélien localement compact métrisable, C. R. Acad. Sci. Paris Sér. I 313 (1991), 345-348. Zbl0738.11052
  11. [11] H. Reiter, Classical Harmonic Analysis and Locally Compact Groups, Clarendon Press, Oxford, 1968. Zbl0165.15601
  12. [12] W. Rudin, Fourier Analysis on Groups, 2nd ed., Interscience Publishers, New York, 1967. Zbl0698.43001
  13. [13] I. Z. Ruzsa, General multiplicative functions, Acta Arith. 32 (1977), 313-347. Zbl0311.10048
  14. [14] I. Z. Ruzsa, Infinite convolution and shift-convergence of measures on topological groups, in: Probability Measures on Groups (Proc. Conf., Oberwolfach 1981), Lecture Notes in Math. 928, Springer, New York, 1982, 337-353. Zbl0489.60012
  15. [15] A. Weil, L'intégration dans les groupes topologiques et ses applications, 2ème éd., Hermann, Paris, 1965 Zbl0063.08195

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