Zeta Regularized Trigonometric Products Over Zeros Of The Riemann Zeta Function
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914148747575296 |
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| author | Gürel, Efe |
| author_facet | Gürel, Efe |
| contents | We prove a novel zeta regularized product formula concerning regularization of trigonometric products over non-trivial zeros of the Riemann zeta function. Furthermore, we calculate the discrepancies of such regularized products. In special cases, our formula reduces to the Kimoto-Wakayama formula. A conjectural relationship between such products and a weak Riemann hypothesis is speculated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_00723 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Zeta Regularized Trigonometric Products Over Zeros Of The Riemann Zeta Function Gürel, Efe Number Theory 11M41, 11M36, 11M26 We prove a novel zeta regularized product formula concerning regularization of trigonometric products over non-trivial zeros of the Riemann zeta function. Furthermore, we calculate the discrepancies of such regularized products. In special cases, our formula reduces to the Kimoto-Wakayama formula. A conjectural relationship between such products and a weak Riemann hypothesis is speculated. |
| title | Zeta Regularized Trigonometric Products Over Zeros Of The Riemann Zeta Function |
| topic | Number Theory 11M41, 11M36, 11M26 |
| url | https://arxiv.org/abs/2505.00723 |