On Dirichlet Series Involving $\zeta(s)$ and Extensions of the Euler-Mascheroni Constant

Takumi Noda

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arXiv · 2601.19429

On Dirichlet Series Involving $\zeta(s)$ and Extensions of the Euler-Mascheroni Constant

Takumi Noda

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Abstract

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.

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Takumi Noda. 2026-01-27. On Dirichlet Series Involving $\zeta(s)$ and Extensions of the Euler-Mascheroni Constant. https://arxiv.org/abs/2601.19429

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