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arXiv · 1706.08268

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

Aleksandar Ivić
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Abstract

We investigate bounds for the multiplicities $m(β+iγ)$, where $β+iγ\,$ ($β\ge \1/2, γ>0)$ denotes complex zeros of $ζ(s)$. 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 $m(β+iγ)$ is also derived, which is relevant when $β$ 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 $ζ(s)$ and its values over short intervals. https://arxiv.org/abs/1706.08268

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