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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.11405 |
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| _version_ | 1866917301589114880 |
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| author | Candelpergher, B. |
| author_facet | Candelpergher, B. |
| contents | After a brief introduction to Ramanujan's method of summation, we give an expansion of the Riemann Zeta function in the critical strip as a convergent series $\sum_{m\geq 0}x_m P_m(s) $ where the functions $P_m$ are polynomials with their roots on the line $\{\Re(s)=1/2\}$, the coefficients $x_m$ being finite linear combinations of the Euler constant $γ$ and the values $ζ(2),ζ(3),\dots,ζ(m+1).$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_11405 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A new expansion of the Riemann zeta function Candelpergher, B. Number Theory After a brief introduction to Ramanujan's method of summation, we give an expansion of the Riemann Zeta function in the critical strip as a convergent series $\sum_{m\geq 0}x_m P_m(s) $ where the functions $P_m$ are polynomials with their roots on the line $\{\Re(s)=1/2\}$, the coefficients $x_m$ being finite linear combinations of the Euler constant $γ$ and the values $ζ(2),ζ(3),\dots,ζ(m+1).$ |
| title | A new expansion of the Riemann zeta function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.11405 |