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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.18963 |
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Table of Contents:
- In this work, we investigate the positivity of the real part of the log-derivative of the Riemann $ξ$-function in the region $1/2+1/\sqrt{\log t}<σ<1$, where $t$ is sufficiently large. We provide an explicit lower bound for $\mathfrak{R}\sum_ρ1/(s-ρ)$, where the summation runs over the zeta-zeros on the critical line. We also consider hypothetical cases of positivity of the log-derivative of the Riemann $ξ$-function in the provided region, assuming that there are non-trivial zeta-zeros off the critical line.