Abstract

In a recent work J.M. Deshouillers and F. Luca [On the distribution of some means concerning the Euler function, Funct. Approx. Comment. Math. Volume 39, Number 2 (2008), 335-344.] consider certain means of the values of the Euler function to prove that they are dense modulo one. At the Czech-Slovak Number Theory Conference in August 2007, F. Luca raised the question whether certain other sequences of mean values of the Euler function are uniformly distributed modulo one. Among these are the sequences of arithmetic and geometric means. Recently, J.M. Deshouillers and H. Iwaniec gave a method leading to an affirmative answer for Luca's question in the case of arithmetic mean, and a conditional answer for the case of geometric mean. The aim of this talk is to explain this method, and then to use it for studying some more general mean values of the Euler function, and also of the divisor function ó.



Information: