On the series expansion of a square-free zeta series
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911748883218432 |
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| author | Kawalec, Artur |
| author_facet | Kawalec, Artur |
| contents | In this article, we develop a square-free zeta series associated with the Möbius function into a power series, and prove a Stieltjes like formula for these expansion coefficients. We also investigate another analytical continuation of these series and develop a formula for $ζ(\tfrac{1}{2})$ in terms of the Möbius function, and in the last part, we explore an alternating series version of these results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16811 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the series expansion of a square-free zeta series Kawalec, Artur Number Theory In this article, we develop a square-free zeta series associated with the Möbius function into a power series, and prove a Stieltjes like formula for these expansion coefficients. We also investigate another analytical continuation of these series and develop a formula for $ζ(\tfrac{1}{2})$ in terms of the Möbius function, and in the last part, we explore an alternating series version of these results. |
| title | On the series expansion of a square-free zeta series |
| topic | Number Theory |
| url | https://arxiv.org/abs/2312.16811 |