Distribution of the number of square-free divisors in residue classes

L. A. Gromakovskaya, B. M. Shirokov

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

Abstract: The notion of weekly uniform distribution of arithmetical functions was introduced by W. Narckiewicz. The existence problem of that distribution was solved and asymptotic formulas for frequency of hits of function values to residue classes coprime with a module was done for many functions in various papers. That asymptotic formulas contained only principal part of the asymptotic, as rule. Such problem solves for the function which gives the number of square-free divisors of integer, but the asymptotic formula is the asymptotic series.

Keywords: distribution in the residue classes, asymptotic formulas, weekly uniform distribution, number of square-free divisors.

UDC: 511.3

Received: 14.07.2018
Revised: 14.07.2018
Accepted: 18.12.2019

DOI: 10.26907/0021-3446-2020-3-3-11

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:3, 1–8

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