Moments of the Riemann zeta function at its local extrema
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929583785246720 |
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| author | Pearce-Crump, Andrew |
| author_facet | Pearce-Crump, Andrew |
| contents | Conrey, Ghosh and Gonek studied the first moment of the derivative of the Riemann zeta function evaluated at the non-trivial zeros of the zeta function, resolving a problem known as Shanks' conjecture. Conrey and Ghosh studied the second moment of the Riemann zeta function evaluated at its local extrema along the critical line to leading order.
In this paper we combine the two results, evaluating the first moment of the zeta function and its derivatives at the local extrema of zeta along the critical line, giving a full asymptotic. We also consider the factor from the functional equation for the zeta function at these extrema. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05568 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Moments of the Riemann zeta function at its local extrema Pearce-Crump, Andrew Number Theory 11M06 Conrey, Ghosh and Gonek studied the first moment of the derivative of the Riemann zeta function evaluated at the non-trivial zeros of the zeta function, resolving a problem known as Shanks' conjecture. Conrey and Ghosh studied the second moment of the Riemann zeta function evaluated at its local extrema along the critical line to leading order. In this paper we combine the two results, evaluating the first moment of the zeta function and its derivatives at the local extrema of zeta along the critical line, giving a full asymptotic. We also consider the factor from the functional equation for the zeta function at these extrema. |
| title | Moments of the Riemann zeta function at its local extrema |
| topic | Number Theory 11M06 |
| url | https://arxiv.org/abs/2411.05568 |