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On the limit laws of distributions of additive functions

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Abstract

The weak convergence of the frequencies

$$[x]^{-1}\#\{n\leq x, f_x(n)<u\} $$

is considered. Here \(f_x, x\geq 2\), is a set of strongly additive functions and \(f_x(p)\in\{0,1\}\) for all primes p. The description of possible limiting distributions with finite support is found.

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References

  1. Hildebrand, A.: On the limit distribution of discrete random variables. Probab. Th. Rel. Fields 75, 67–76 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  2. Levin, B.V., Timofeev, N.M.: On the distribution of values of additive function. Acta Arith. 26(4), 333–364 (1975)

    MATH  MathSciNet  Google Scholar 

  3. Petrov, V.V.: Sums of Independent Random Variables. Springer-Verlag, New York, Heidelberg, Berlin (1975)

    MATH  Google Scholar 

  4. Rusza, I.Z.: Generalizations of Kubilius class of additive functions. I. In: New Trends in Probab. and Statistics, vol. 2. Analytic and Probabilistic Methods in Number Theory, Proceedings of the Intern. Conf. in Honour of J. Kubilius, Palanga, Lithuania, 24–28 September 1991 (eds. F. Schweiger and E. Manstavičius), vsp/TEV, Utrecht/Vilnius, pp. 269–283 (1992)

  5. Šiaulys, J.: Factorial moments of distributions of additive functions. LMJ 40(4), 389–408 (2000)

    Google Scholar 

  6. Šiaulys, J.: On the separation of distributions of additive functions. In: Analytic and Probabilistic Methods in Number Theory, Proceedings of the Third Intern. Conf. in Honour of J. Kubilius, Palanga, Lithuania, 24–28 September 2001 (eds. A. Dubickas, A. Laurinčikas and E. Manstavičius), TEV, Vilnius, pp. 297–302 (2002)

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Vilnius University, Naugarduko 24, 2600, Vilnius, Lithuania

    Jonas Šiaulys & Algirdas Mačiulis

Authors
  1. Jonas Šiaulys
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  2. Algirdas Mačiulis
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Correspondence to Algirdas Mačiulis.

Additional information

2000 Mathematics Subject Classification Primary—11K65; Secondary—11N37, 11N60, 60F05

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Šiaulys, J., Mačiulis, A. On the limit laws of distributions of additive functions. Ramanujan J 12, 167–183 (2006). https://doi.org/10.1007/s11139-006-0071-5

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  • DOI: https://doi.org/10.1007/s11139-006-0071-5

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