Geodesic
On~the zeros of the function $\zeta(s)$ on short intervals of the critical line
Izvestiya. Mathematics , Tome 24 (1985) no. 3, pp. 523-537

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It is proved that for any $\varepsilon>0$ there exists $c=c(\varepsilon)>0$ such that for $T\geqslant T_0(\varepsilon)>0$ and $H=T^{27/82+\varepsilon}$ we have $N_0(T+H)-N_0(T)\geqslant cH\ln T$, where $N_0(T)$ is the number of odd order zeros of $\zeta(\frac12+it)$ in the interval $(0,T)$. Bibliography: 12 titles. 
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     author = {A. A. Karatsuba},
     title = {On~the zeros of the function $\zeta(s)$ on short intervals of the critical line},
     journal = {Izvestiya. Mathematics },
     pages = {523--537},
     publisher = {mathdoc},
     volume = {24},
     number = {3},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_24_3_a3/}
}
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A. A. Karatsuba. On~the zeros of the function $\zeta(s)$ on short intervals of the critical line. Izvestiya. Mathematics , Tome 24 (1985) no. 3, pp. 523-537. http://geodesic.mathdoc.fr/item/IM2_1985_24_3_a3/