Geodesic
Sign changes of the function $S(t)$ on short intervals
Izvestiya. Mathematics , Tome 69 (2005) no. 4, pp. 719-731

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In this paper, we study sign changes of the function $S(t)$ on short intervals of the real line. It is proved that, for almost all values of $T$, there is a point at which $S(t)$ changes sign and whose distance from $T$ does not exceed $4.39\ln\ln\ln\ln T$. 
@article{IM2_2005_69_4_a3,
     author = {M. A. Korolev},
     title = {Sign changes of the function $S(t)$ on short intervals},
     journal = {Izvestiya. Mathematics },
     pages = {719--731},
     publisher = {mathdoc},
     volume = {69},
     number = {4},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a3/}
}
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M. A. Korolev. Sign changes of the function $S(t)$ on short intervals. Izvestiya. Mathematics , Tome 69 (2005) no. 4, pp. 719-731. http://geodesic.mathdoc.fr/item/IM2_2005_69_4_a3/