On the multiplicities of zeros of ζ(s) and its values over short intervals
We investigate bounds for the multiplicities m(β+iγ), where β+iγ (β⩾12,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 re...
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Published in | Journal of number theory Vol. 185; pp. 65 - 79 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Elsevier Inc
01.04.2018
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Subjects | |
Online Access | Get full text |
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Summary: | We investigate bounds for the multiplicities m(β+iγ), where β+iγ (β⩾12,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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ISSN: | 0022-314X 1096-1658 |
DOI: | 10.1016/j.jnt.2017.09.017 |