On the multiplicites of zeros of $\zeta(s)$ and its values over short intervals
| Autor: | Ivić, Aleksandar |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 15 pages |
| Databáze: | arXiv |
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