Evaluating ζ(s) At Odd Positive Integers Using Automatic Dirichlet Series

2025/08/06 by Tóth, László
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.04151

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 π. In doing so, we also provide an alternative proof of a 2015 result by Allouche and Sondow.

Citations

• Identities inspired from the Ramanujan Notebooks, first series (1998)

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