On an Asymptotic Property of Divisor τ-Function

T. Hakobyan, S. Vostokov

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper for μ > 0 we study an asymptotic behavior of the sequence defined as Tn(μ) = (τ(n))−1max1≤t≤[n1/μ] {τ(n + t)}, where τ(n) denotes the number of natural divisors of given positive integer n. The motivation of this observation is to explore whether τ-function oscillates rapidly.

Original languageEnglish
Pages (from-to)77-83
Number of pages7
JournalLobachevskii Journal of Mathematics
Volume39
Issue number1
DOIs
StatePublished - 1 Jan 2018

Scopus subject areas

  • Mathematics(all)

Keywords

  • Derichlet’s divisor problem
  • divisor
  • Prime Number Theorem
  • Stirling’s formula
  • τ-function

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