Trigonometric Selector Kernels, Duality, and Odd Zeta Values
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914035934429184 |
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| author | Nagai, Ken |
| author_facet | Nagai, Ken |
| contents | In this short note, we develop trigonometric selector kernels to represent odd zeta values via dual hyperbolic counterparts. This framework highlights a Fourier-Poisson duality, incorporating finite-part integrals in the sense of Hadamard-Galapon. In particular, we show how such kernels naturally recover Euler-Maclaurin and Poisson summation formulas as dual manifestations. We further connect our kernel approach with the finite-part integral formulation, extending earlier Cvijović-Klinowski type representations for odd zeta values. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10801 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trigonometric Selector Kernels, Duality, and Odd Zeta Values Nagai, Ken General Mathematics In this short note, we develop trigonometric selector kernels to represent odd zeta values via dual hyperbolic counterparts. This framework highlights a Fourier-Poisson duality, incorporating finite-part integrals in the sense of Hadamard-Galapon. In particular, we show how such kernels naturally recover Euler-Maclaurin and Poisson summation formulas as dual manifestations. We further connect our kernel approach with the finite-part integral formulation, extending earlier Cvijović-Klinowski type representations for odd zeta values. |
| title | Trigonometric Selector Kernels, Duality, and Odd Zeta Values |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2509.10801 |