Some Remarks on the Distribution of a Sequence Connected with $\zeta(\frac12)$

Abstract

As a complement to a recent paper by Jade Vinson we study the distribution of the sequence $(\sum_{j=1}^n j^{-s})_{n\ge1}$ modulo 1 with the aim of explaining its different behaviour when $s=\frac12$ and when $\frac12<s<1$. We tackle this question from a different point of view using the theory of uniformly distributed sequences.