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 
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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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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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