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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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/

[1] Riman B., Sochineniya, OGIZ, M., L., 1948

[2] Hardy G. H., “Sur les zeros de la fonction $\zeta(s)$ de Riemann”, Compt. Rend. Acad. Sci., 158 (1914), 1012–1014 | Zbl

[3] Hardy G. H., Littlewood J. E., “Contributions to the theory of Riemann zeta-function and the theory of distribution of primes”, Acta Math., 41 (1918), 119–196 | DOI | MR

[4] Hardy G. H., Littlewood J. E., “The zeros of Riemann's zeta-function on the critical line”, Math. Zs., 10 (1921), 283–317 | DOI | MR | Zbl

[5] Selberg A., “On the zeros of Riemann's zeta-function”, Skr. Norske Vid. Akad. Oslo, 10 (1942) | MR

[6] Mozer Ya., “Ob odnoi teoreme Khardi–Littlvuda v teorii dzeta-funktsii Rimana”, Acta Arith., 31 (1976), 45–51 | MR

[7] Mozer Ya., “O kornyakh uravneniya $Z'(t)=0$”, Acta Arith., 40 (1981), 79–89, 97–107 | MR

[8] Mozer Ya., “Uluchshenie teoremy Khardi–Littlvuda o plotnosti nulei funktsii $\zeta(1/2+it)$”, Acta Math. Univ. Comen. Bratislava, 42,43 (1983), 41–50 | MR

[9] Karatsuba A. A., “O rasstoyanii mezhdu sosednimi nulyami dzeta-funktsii Rimana, lezhaschimi na kriticheskoi pryamoi”, Tr. Matem., in-ta im. V. A. Steklova AN SSSR, 157, 1981, 49–63 | MR | Zbl

[10] Karatsuba A. A., “O nulyakh dzeta-funktsii Rimana na korotkikh promezhutkakh kriticheskoi pryamoi”, Dokl. AN SSSR, 272:6 (1983), 1312–1314 | MR | Zbl

[11] Titchmarsh E. K., Teoriya dzeta-funktsii Rimana, IL, M., 1953

[12] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, 2-e izd., Nauka, M., 1983 | MR