Uniformity of distribution modulo 1 of the geometric mean prime divisor

Florian Luca*, Igor E. Shparlinski

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the fractional parts of n1/ω(n), n 1/Ω(n) and the geometric mean of the distinct prime factors of n are uniformly distributed modulo 1 as n ranges over all the positive integers, where Ω(n) and ω(n) denote the number of distinct prime divisors of n counted with and without multiplicities. Note that n1/Ω(n) is the geometric mean of all prime divisors of n taken with the corresponding multiplicities. The result complements a series of results of similar spirit obtained by various authors, while the method can be applied to several other arithmetic functions of similar structure.

Original languageEnglish
Pages (from-to)155-163
Number of pages9
JournalBoletin de la Sociedad Matematica Mexicana
Volume12
Issue number2
Publication statusPublished - Oct 2006

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