%0 Journal Article
%T On the distribution modulo one of the mean values of some arithmetical functions
%A Jean-Marc Deshouillers
%A Henryk Iwaniec
%J Uniform Distribution Theory
%D 2008
%I Mathematical Institute of the Slovak Academy of Sciences
%X Florian Luca asked whether the sequence consisting of the arithmetic(extit {resp.} geometric) mean values of the Euler $ \varphi$ functionis uniformly distributed modulo $1$. We show that it is the case for the arithmetic means, and that it is the case for the geometric means if and only if the number $e^{-1} \prod_p (1-1/p)^{1/p}$ is irrational. More general arithmetic functions are also considered.
%K Euler function
%K distribution modulo $1$
%K multiplicative functions
%U http://www.boku.ac.at/MATH/udt/vol03/no1/DesIwa08-1.pdf