Geodesic
The Argument of the Riemann Zeta Function on the Critical Line
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 215-238
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The following assertion is proved: If $N_1(T)$ is the number of sign changes of the argument of the Riemann zeta function $\zeta (s)$ on the interval $0\operatorname{Im}s\le T$ of the critical line$\operatorname{Re}s=1/2$, then, for any $a$ such that $27/82$, $T\ge T_1(a)>0$, and $H=T^a$, the inequality $N_1(T+H)-N_1(T) \ge H\log T\exp \bigl (-\frac {c\log \log T}{\sqrt {\log \log \log T}}\bigr )$ holds with a constant $c=c(a)>0$. 
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M. A. Korolev. The Argument of the Riemann Zeta Function on the Critical Line. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Discrete geometry and geometry of numbers, Tome 239 (2002), pp. 215-238. http://geodesic.mathdoc.fr/item/TM_2002_239_a13/

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