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Distribution of the Number of Square-Free Divisors in Residue Classes

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Abstract

The notion of weekly uniform distribution of arithmetical functions was introduced by W. Narckiewicz. For many functions in various papers, the problem of existence of such distribution was solved, and asymptotic formulas for frequency of hits of function values in residue classes coprime with a module were established. These asymptotic formulas contained, as a rule, only principal part of the asymptotics. A similar problem is solved in the present paper for the function which gives the number of square-free divisors of a natural number, but the asymptotic formula is the asymptotic series.

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Authors and Affiliations

  1. Petrozavodsk State University, 33 Lenin Ave., Petrozavodsk, 185910, Russia

    L. A. Gromakovskaya & B. M. Shirokov

Authors
  1. L. A. Gromakovskaya
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  2. B. M. Shirokov
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Corresponding authors

Correspondence to L. A. Gromakovskaya or B. M. Shirokov.

Additional information

Russian Text © The Author(s), 2020, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 3, pp. 3–11.

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Gromakovskaya, L.A., Shirokov, B.M. Distribution of the Number of Square-Free Divisors in Residue Classes. Russ Math. 64, 1–8 (2020). https://doi.org/10.3103/S1066369X20030019

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  • DOI: https://doi.org/10.3103/S1066369X20030019

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