Uniform distribution of sequences involving divisor function

Mehdi Hassani

Vol. 18 No. 1 (2013)

Regular Articles

Uniform distribution of sequences involving divisor function

Mehdi Hassani

Submission of an original manuscript to the Mathematical Communications will be taken to mean that it represents original work not previously published, that it is not being considered elsewhere for publication; and, if accepted for publication, it will be published in print and online form and it will not be published elsewhere in the same form, for commercial purposes, in any language, without the consent of the publisher. The journal takes the stance that the publication of scholarly research is meant to disseminate knowledge and, in a not-for-profit regime, benefits neither publisher nor author financially. It sees itself as having an obligation to its authors and to society to make content available online now that the technology allows for such a possibility.

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 $\f$.

PDF