Evaluating $ζ(s)$ At Odd Positive Integers Using Automatic Dirichlet Series
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911093918531584 |
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| author | Tóth, László |
| author_facet | Tóth, László |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04151 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Evaluating $ζ(s)$ At Odd Positive Integers Using Automatic Dirichlet Series Tóth, László Number Theory 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. |
| title | Evaluating $ζ(s)$ At Odd Positive Integers Using Automatic Dirichlet Series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.04151 |