Smooth Values of the Iterates of the Euler Phi-Function

Lamzouri, Youness

Canadian journal of mathematics, Tome 59 (2007) no. 1, pp. 127-147

Résumé

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

Détail

DOI : 10.4153/CJM-2007-006-4

Mots-clés : 11N37, 11B37, 34K05, 45J05

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