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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     author = {A. A. Karatsuba},
     title = {On~the zeros of the function $\zeta(s)$ in the neighborhood of the critical line},
     journal = {Izvestiya. Mathematics },
     pages = {307--313},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a3/}
}
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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/