On the Zeros of the Riemann Zeta Function of Large Multiplicity
Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 652-657.

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We obtain a new upper bound for the number of zeros of the Riemann zeta function of a given multiplicity lying in a given rectangle of the critical strip.
Keywords: Riemann zeta function, zeros of the Riemann zeta function, Fujii's inequality, Lagrange's mean-value theorem.
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R. N. Boyarinov. On the Zeros of the Riemann Zeta Function of Large Multiplicity. Matematičeskie zametki, Tome 89 (2011) no. 5, pp. 652-657. http://geodesic.mathdoc.fr/item/MZM_2011_89_5_a1/

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[3] A. Fujii, “On the distribution of the zeros of the Riemann zeta function in short intervals”, Bull. Amer. Math. Soc., 81:1 (1975), 139–142 | DOI | MR | Zbl