Some Remarks on the Distribution of a Sequence Connected with ζ(½)

Abstract

As a complement to a recent paper by Jade Vinson we study the distribution of the sequence (Σⁿ _j=1 j ⁻⁸)n?l modulo 1 with the aim of explaining its different behaviour when s = ½ and when ½ < s < 1. We tackle this question from a different point of view using the theory of uniformly distributed sequences.

Keywords:

• Riemann zeta-function
• uniform distribution
• discrepancy