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arXiv · 1706.08268

On the multiplicites of zeros of $\zeta(s)$ and its values over short intervals

Aleksandar Ivić
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Abstract

We investigate bounds for the multiplicities $m(\beta+i\gamma)$, where $\beta+i\gamma\,$ ($\beta\ge \1/2, \gamma>0)$ denotes complex zeros of $\zeta(s)$. It is seen that the problem can be reduced to the estimation of the integrals of the zeta-function over "very short" intervals. A new, explicit bound for $m(\beta+i\gamma)$ is also derived, which is relevant when $\beta$ is close to unity. The related Karatsuba conjectures are also discussed.

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Aleksandar Ivić. 2017-06-26. On the multiplicites of zeros of $\zeta(s)$ and its values over short intervals. https://arxiv.org/abs/1706.08268

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