On Dirichlet Series Involving $ζ(s)$ and Extensions of the Euler-Mascheroni Constant
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914330804486144 |
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| author | Noda, Takumi |
| author_facet | Noda, Takumi |
| contents | In this paper, we introduce a class of Dirichlet series defined in terms of the Riemann zeta-function, motivated by the study of their special values, and establish integral representations for these series. We also define an extension of the Euler--Mascheroni constant and express certain special values explicitly in terms of the Bendersky constants. These results provide a unified framework for evaluating Dirichlet series involving the Riemann zeta-function at integer arguments, together with the associated number-theoretic constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_19429 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Dirichlet Series Involving $ζ(s)$ and Extensions of the Euler-Mascheroni Constant Noda, Takumi Number Theory In this paper, we introduce a class of Dirichlet series defined in terms of the Riemann zeta-function, motivated by the study of their special values, and establish integral representations for these series. We also define an extension of the Euler--Mascheroni constant and express certain special values explicitly in terms of the Bendersky constants. These results provide a unified framework for evaluating Dirichlet series involving the Riemann zeta-function at integer arguments, together with the associated number-theoretic constants. |
| title | On Dirichlet Series Involving $ζ(s)$ and Extensions of the Euler-Mascheroni Constant |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.19429 |