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Lithuanian Mathematical Journal

, Volume 58, Issue 2, pp 235–248 | Cite as

Discrete Uniform Limit Law for a Sum of Additive Functions on Shifted Primes

  • Jonas Šiaulys
  • Gediminas Stepanauskas
  • Laura Žvinytė
Article

Abstract

We consider the limit distribution of a sum of strongly additive arithmetic functions with arguments running

through shifted primes. We obtain sufficient and necessary conditions for the weak convergence of distributions of such sums to the discrete uniform law. We study the case where the functions take values 0 or 1 on primes.

Keywords

additive function discrete uniform distribution frequency weak convergence 

MSC

11K65 11N37 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Jonas Šiaulys
    • 1
  • Gediminas Stepanauskas
    • 1
  • Laura Žvinytė
    • 1
  1. 1.Institute of MathematicsVilnius UniversityVilniusLithuania

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