On the zeros of the function $\zeta(s)$ on short intervals of the critical line

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.