Evaluating $\zeta(s)$ At Odd Positive Integers Using Automatic Dirichlet Series
Number Theory
2025-08-07 v1
Abstract
In this paper, we use the Thue-Morse sequence and the paperfolding sequence to build a Dirichlet series that evaluates to a linear combination of the Riemann zeta function at odd positive integers and odd powers of . In doing so, we also provide an alternative proof of a 2015 result by Allouche and Sondow.
Cite
@article{arxiv.2508.04151,
title = {Evaluating $\zeta(s)$ At Odd Positive Integers Using Automatic Dirichlet Series},
author = {László Tóth},
journal= {arXiv preprint arXiv:2508.04151},
year = {2025}
}