Irrational Factor of Order k and ITS Connections With k-Free Integers

D. Dong, X. Meng*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce an irrational factor of order k defined by (Formula presented.), where (Formula presented.) is the factorization of n and (Formula presented.). It turns out that the function (Formula presented.) well approximates the characteristic function of k-free integers. We also derive asymptotic formulas for (Formula presented.) and (Formula presented.).

Original languageEnglish (US)
Pages (from-to)353-366
Number of pages14
JournalActa Mathematica Hungarica
Volume144
Issue number2
DOIs
StatePublished - Nov 1 2014
Externally publishedYes

Keywords

  • asymptotic formula
  • Dirichlet series
  • irrational factor
  • k-free number
  • Perron’s formula
  • Riemann zetafunction

ASJC Scopus subject areas

  • Mathematics(all)

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