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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.22421 |
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Table of Contents:
- The evaluation of the Riemann zeta function at negative integers is a classical result typically obtained through analytic continuation or contour integration. In this paper, we present a novel and concise derivation of these special values by employing the theory of Cesàro limit of distributions, a generalized limit concept developed by Estrada, Kanwal, and Fulling. We use this tool to give a quick proof of the result that \[ ζ(-n)=-\frac{B_{n+1}}{n+1}, \] for $n\in\mathbb{N}^+.$ We also give a short discussion on $ζ^{\prime }(α)$ and compute the value of $ζ^{\prime}(0)$.