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On the Local Distance between Arithmetical Distributions

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Abstract

We obtain upper and lower bounds for the local distance ρ(v x , P x ). Here v x is the distribution of a set of strongly additive functions f x with respect to the usual frequency on the set of positive integers, and P x is the distribution of the sum of suitably chosen independent random variables. We only consider the case where f x (p) ∈ {0, 1} for all primes p.

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REFERENCES

  1. J. Kubilius, Probabilistic Methods in the Theory of Numbers, Amer. Math. Soc. Transl. Math. Monographs, 11, Providence (1964).

  2. P. D. T. A. Elliott, Probabilistic Number Theory. I, Springer, Berlin (1979).

    Google Scholar 

  3. P. D. T. A. Elliott, Probabilistic Number Theory. II, Springer, Berlin (1980).

    Google Scholar 

  4. G. Tenenbaum, Crible d'Eratosthene et modele de Kubilius, in: Number Theory in Progress. Proceedings of the International Conference Organized by the Stefan Banach International Mathematical Center in honor of the 60th Birthday of Andrzej Schinzel, Elementary and Analytic Number Theory, Vol. 2, K. Gyory et al. (Eds.), Walter de Gruyter, Berlin (1999), pp. 1099–1129.

    Google Scholar 

  5. G. Halasz, On the distribution of additive arithmetic functions, Acta Arithm., 27, 143–152 (1975).

    MATH  MathSciNet  Google Scholar 

  6. J. Siaulys and G. Stepanauskas, Kubilius-type sequences of additive functions, Lith. Math. J., 45(2), 225–234 (2005).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Vilnius University, Naugarduko 24, LT-03225, Vilnius, Lithuania

    J. Siaulys & A. Maciulis

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  1. J. Siaulys
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  2. A. Maciulis
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Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 603–610, October–December, 2005.

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Siaulys, J., Maciulis, A. On the Local Distance between Arithmetical Distributions. Lith Math J 45, 487–492 (2005). https://doi.org/10.1007/s10986-006-0010-6

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  • DOI: https://doi.org/10.1007/s10986-006-0010-6

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