Evaluating $\zeta(s)$ At Odd Positive Integers Using Automatic Dirichlet Series

László Tóth

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arXiv · 2508.04151

Evaluating $\zeta(s)$ At Odd Positive Integers Using Automatic Dirichlet Series

László Tóth

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

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László Tóth. 2025-08-06. Evaluating $\zeta(s)$ At Odd Positive Integers Using Automatic Dirichlet Series. https://arxiv.org/abs/2508.04151

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