Lobachevskii Journal of Mathematics

, Volume 39, Issue 1, pp 77–83 | Cite as

On an Asymptotic Property of Divisor τ-Function

  • T. Hakobyan
  • S. Vostokov


In this paper for μ > 0 we study an asymptotic behavior of the sequence defined as T n (μ) = (τ(n))−1\({\max _{1 \leqslant t \leqslant \left[ {{n^{1/\mu }}} \right]}}\) {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.

Keywords and phrases

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


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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