Uniform distribution of sequences involving divisor function

Abstract

We modify the recent method of J.-M. Deshouillers and H. Iwaniec
in the theory of uniform distribution to show that the sequence with
general term $a_n=\frac{1}{n}\sum_{m\leq n}\si(m)$ is uniformly
distributed modulo 1. We also study uniform distribution modulo 1
of some sequences related by the functions $\si$ and $\f$.