Mean values of the Riemann zeta function at shifted zeros under the Riemann Hypothesis
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911299530653696 |
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| author | Garunkštis, Ramūnas Paliulionytė, Julija |
| author_facet | Garunkštis, Ramūnas Paliulionytė, Julija |
| contents | Assuming the Riemann hypothesis, we obtain asymptotic formulas for $\sum_{0<γ<T}ζ(ρ+δ)ζ(1-ρ+\overlineδ)$ in the region $-\frac{a}{\log T} \leq \Re δ\leq \frac{1}{2}+\frac{a}{\log T}$, $|\Im δ|\ll 1$. Unconditionally, this asymptotic formula was recently obtained by Garunkštis and Novikas in essentially the same region, with a slight incompleteness. Assuming RH, we obtain a sharper error term, and we also correct an inaccuracy in the unconditional error term there. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03297 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mean values of the Riemann zeta function at shifted zeros under the Riemann Hypothesis Garunkštis, Ramūnas Paliulionytė, Julija Number Theory 11M06 Assuming the Riemann hypothesis, we obtain asymptotic formulas for $\sum_{0<γ<T}ζ(ρ+δ)ζ(1-ρ+\overlineδ)$ in the region $-\frac{a}{\log T} \leq \Re δ\leq \frac{1}{2}+\frac{a}{\log T}$, $|\Im δ|\ll 1$. Unconditionally, this asymptotic formula was recently obtained by Garunkštis and Novikas in essentially the same region, with a slight incompleteness. Assuming RH, we obtain a sharper error term, and we also correct an inaccuracy in the unconditional error term there. |
| title | Mean values of the Riemann zeta function at shifted zeros under the Riemann Hypothesis |
| topic | Number Theory 11M06 |
| url | https://arxiv.org/abs/2512.03297 |