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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.08121 |
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| _version_ | 1866912579226435584 |
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| author | Hughes, Christopher Pearce-Crump, Andrew |
| author_facet | Hughes, Christopher Pearce-Crump, Andrew |
| contents | We conjecture results about the moments of mixed derivatives of the Riemann zeta function, evaluated at the non-trivial zeros of the Riemann zeta function. We do this in two different ways, both giving us the same conjecture. In the first, we find asymptotics for the moments of derivatives of the characteristic polynomials of matrices in the Circular Unitary Ensemble. In the second, we consider the hybrid model approach first proposed by Gonek, Hughes and Keating. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_08121 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moments of derivatives of the Riemann zeta function: Characteristic polynomials and the hybrid formula Hughes, Christopher Pearce-Crump, Andrew Number Theory We conjecture results about the moments of mixed derivatives of the Riemann zeta function, evaluated at the non-trivial zeros of the Riemann zeta function. We do this in two different ways, both giving us the same conjecture. In the first, we find asymptotics for the moments of derivatives of the characteristic polynomials of matrices in the Circular Unitary Ensemble. In the second, we consider the hybrid model approach first proposed by Gonek, Hughes and Keating. |
| title | Moments of derivatives of the Riemann zeta function: Characteristic polynomials and the hybrid formula |
| topic | Number Theory |
| url | https://arxiv.org/abs/2406.08121 |