Resolution Of Multiplicative Anomaly Of Zeta Regularization For Polynomials
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914018003779584 |
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| author | Gürel, Efe |
| author_facet | Gürel, Efe |
| contents | In this paper, the problem of multiplicative anomaly of zeta regularization is solved for polynomials. For a regularizable sequence $Λ$, we explicitly calculate the zeta regularized product of $(Λ-z_1)\dots(Λ-z_n)$ for $z_1,\dots,z_n\in\mathbb{C}$. We give an explicit formula for the discrepancies between polynomials. Our results imply Mizuno's theorem as a special case. We furthermore give novel regularized product formulas for multi-dimensional products in terms of Barnes multiple gamma functions, zeros of the Riemann zeta function and zeros of the Bessel function of the first kind. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_14563 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Resolution Of Multiplicative Anomaly Of Zeta Regularization For Polynomials Gürel, Efe Number Theory Mathematical Physics 11M36 In this paper, the problem of multiplicative anomaly of zeta regularization is solved for polynomials. For a regularizable sequence $Λ$, we explicitly calculate the zeta regularized product of $(Λ-z_1)\dots(Λ-z_n)$ for $z_1,\dots,z_n\in\mathbb{C}$. We give an explicit formula for the discrepancies between polynomials. Our results imply Mizuno's theorem as a special case. We furthermore give novel regularized product formulas for multi-dimensional products in terms of Barnes multiple gamma functions, zeros of the Riemann zeta function and zeros of the Bessel function of the first kind. |
| title | Resolution Of Multiplicative Anomaly Of Zeta Regularization For Polynomials |
| topic | Number Theory Mathematical Physics 11M36 |
| url | https://arxiv.org/abs/2504.14563 |