Extremal orders of compositions of certain arithmetical functions

József Sándor; László Tóth

Extremal orders of compositions of certain arithmetical functions

Number Theory 2008-09-01 v2

Authors: József Sándor , László Tóth

Abstract

We study the exact extremal orders of compositions $f(g(n))$ of certain arithmetical functions, including the functions $\sigma(n)$ , $\phi(n)$ , $\sigma^*(n)$ and $\phi^*(n)$ , representing the sum of divisors of $n$ , Euler's function and their unitary analogues, respectively. Our results complete, generalize and refine known results.

Keywords

special functions multiplicative functions function spaces and inequalities

Cite

@article{arxiv.0802.1106,
  title  = {Extremal orders of compositions of certain arithmetical functions},
  author = {József Sándor and László Tóth},
  journal= {arXiv preprint arXiv:0802.1106},
  year   = {2008}
}

Comments

improved and corrected final version

Related papers

View all related →