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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2201.08599 |
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Table of Contents:
- In this paper we investigate the positivity property of the real part of logarithmic derivative of the Riemann $ξ$-function for $1/2<σ<1$ and sufficiently large $t$. We give an explicit upper and lower bounds for $\Re\sum_ρ 1/(s-ρ)$, where the sum runs over the zeros of $ζ(s)$ on the line $1/2+it$. We also check the positivity of $\Re ξ'/ξ(s)$ for $1/2<σ<1$ assuming that there occur a non-trivial zeros of $ζ(s)$ off the critical line.