Smooth values of the iterates of the Euler's Phi function

Youness Lamzouri

Smooth values of the iterates of the Euler's Phi function

Number Theory 2010-05-26 v1

Authors: Youness Lamzouri

Abstract

Let $\phi(n)$ be the Euler-phi function, define $\phi_0(n) = n$ and $\phi_{k+1}(n)=\phi(\phi_{k}(n))$ for all $k\geq 0$ . We will determine an asymptotic formula for the set of integers $n$ less than $x$ for which $\phi_k(n)$ is $y$ -smooth, conditionally on a weak form of the Elliott-Halberstam conjecture.

Keywords

multiplicative functions divisor function

Cite

@article{arxiv.math/0503246,
  title  = {Smooth values of the iterates of the Euler's Phi function},
  author = {Youness Lamzouri},
  journal= {arXiv preprint arXiv:math/0503246},
  year   = {2010}
}

Comments

20 pages, see also http://www.dms.umontreal.ca/~lamzouri

Related papers

View all related →