Geodesic
On~the zeros of the function $\zeta(s)$ in the neighborhood of the critical line
Izvestiya. Mathematics , Tome 26 (1986) no. 2, pp. 307-313.

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The following theorem is proved. If $H\geqslant T^a$, where $T>T_0>0$ and $a>27/82$, then for $1/2\sigma\leqslant1$ the estimate $$ N(\sigma,T+H)-N(\sigma,T)=O\biggl(\frac{H}{\sigma-0.5}\biggr) $$ holds uniformly in $\sigma$, where $N(\sigma_1,t)$ denotes the number of zeros $s=\sigma+it$, with $\sigma>\sigma_1$ and $0$, of the Riemann zeta-function $\zeta(s)$. Bibliography: 4 titles. 
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     title = {On~the zeros of the function $\zeta(s)$ in the neighborhood of the critical line},
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A. A. Karatsuba. On~the zeros of the function $\zeta(s)$ in the neighborhood of the critical line. Izvestiya. Mathematics , Tome 26 (1986) no. 2, pp. 307-313. http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a3/

[1] Mangoldt H., “Zur Verteilung der Nullstellen der Riemannschen Funktion $\zeta(t)$”, Math. Annalen, 60 (1905), 1–19 | DOI | Zbl

[2] Littlewood J. E., “On the zeros of Riemann zeta-function”, Proc. Camb. Phil. Soc., 22 (1924), 295–318 | DOI | Zbl

[3] Selberg A., “On the zeros of Riemann's zeta-funktion”, Skr. Norske Vid. Akad. Oslo I, 10 (1942), 1–59 | MR

[4] Karatsuba A. A., “O nulyakh funktsii $\zeta(s)$ na korotkikh promezhutkakh kriticheskoi pryamoi”, Izv. AN SSSR. Ser. matem., 48:3 (1984), 569–584 | MR | Zbl