The discrete second moment of mixed derivatives of the Riemann zeta function
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914244730028032 |
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| author | Durkan, Benjamin Hughes, Christopher Pearce-Crump, Andrew |
| author_facet | Durkan, Benjamin Hughes, Christopher Pearce-Crump, Andrew |
| contents | We establish the full asymptotic for the discrete second moment of the Riemann zeta function of mixed derivatives evaluated at the zeta zeros, providing both unconditional and conditional error terms. This was first studied by Gonek, where only the leading order asymptotic was given, later extended by Conrey--Snaith and Milinovich to include the lower order terms for the first derivative. We extend the case of the first derivative to all derivatives. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06292 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The discrete second moment of mixed derivatives of the Riemann zeta function Durkan, Benjamin Hughes, Christopher Pearce-Crump, Andrew Number Theory 11M06 We establish the full asymptotic for the discrete second moment of the Riemann zeta function of mixed derivatives evaluated at the zeta zeros, providing both unconditional and conditional error terms. This was first studied by Gonek, where only the leading order asymptotic was given, later extended by Conrey--Snaith and Milinovich to include the lower order terms for the first derivative. We extend the case of the first derivative to all derivatives. |
| title | The discrete second moment of mixed derivatives of the Riemann zeta function |
| topic | Number Theory 11M06 |
| url | https://arxiv.org/abs/2601.06292 |