Lithuanian Mathematical Journal

, Volume 51, Issue 4, pp 562–572 | Cite as

Binomial limit law for additive prime indicators



We obtain criteria for the weak convergence of distributions of a set of strongly additive functions f x to the binomial law. We consider the case where f x (p)∈{0, 1} for every prime p. Some examples are presented.


additive function binomial law frequency weak convergence 




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P.D.T.A. Elliott, Probabilistic Number Theory, I, Springer-Verlag, New York, 1979.MATHCrossRefGoogle Scholar
  2. 2.
    P.D.T.A. Elliott, Probabilistic Number Theory, II, Springer-Verlag, New York, 1980.MATHGoogle Scholar
  3. 3.
    J. Kubilius, Probabilistic Methods in the Theory of Numbers, Transl. Math. Monogr., Vol. 11, Amer. Math. Soc., Providence, RI, 1964.MATHGoogle Scholar
  4. 4.
    A. Mačiulis and J. Šiaulys, On the limit laws of distributions of additive functions, Ramanujan J., 12:167–183, 2006.MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    J. Šiaulys, On the distributions of additive functions, in Lietuvos Matematikų Draugijos Mokslo Darbai, Vol. 3 (special issue of Liet. Mat. Rink.), Institute of Mathematics and Informatics, Vilnius, 1999, pp. 104–109.Google Scholar
  6. 6.
    J. Šiaulys, Factorial moments of distributions of additive functions, Liet. Mat. Rink., 40(4):508–525, 2000 (in Russian). English transl.: Lith. Math. J., 40(4):389–401, 2000.MATHCrossRefGoogle Scholar
  7. 7.
    J. Šiaulys and G. Stepanauskas, Some limit laws for strongly additive prime indicators, Šiauliai Math. Semin., 3(11):235–246, 2008.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2011

Authors and Affiliations

  1. 1.Faculty of Mathematics and InformaticsVilnius UniversityVilniusLithuania

Personalised recommendations