On the function~$S(t)$
Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 901-931.

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We prove a theorem on the density of zeros of the Riemann function $\zeta(s)$ in narrow rectangles of neighbourhoods of the critical line and theorems on moments and the number of changers of sign of $S(t)$ on short intervals on the real line.
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A. A. Karatsuba. On the function~$S(t)$. Izvestiya. Mathematics , Tome 60 (1996) no. 5, pp. 901-931. http://geodesic.mathdoc.fr/item/IM2_1996_60_5_a3/

[1] Selberg A., “Contributions to the theory of the Riemann zeta-function”, Archiv für Mathematik og Naturvidenskab, XLVIII:5 (1946), 89–155 | MR

[2] Selberg A., “On the zeros of Riemann's zeta-function”, Skr. Norske Vid. Akad. Oslo, 10 (1942), 1–59 | MR

[3] Selberg A., “On the remainder in the formula for $N(T)$, the number of zeros of $\zeta (s)$ in the strip $0$”, Avhandlinger Norske Vid. Akad. Oslo, 1944, no. 1 | MR

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

[5] Karatsuba A. A., “O nulyakh funktsii $\zeta (s)$ na korotkikh promezhutkakh kriticheskoi pryamoi”, Izv. AN SSSR. Ser. matem., 48:3 (1984), 569–584 | MR | Zbl

[6] Karatsuba A. A., “O nulyakh funktsii $\zeta (s)$ v okrestnosti kriticheskoi pryamoi”, Izv. AN SSSR. Ser. matem., 49:2 (1985), 326–333 | MR

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

[8] Hardy G. H., Littlewood J. E., “The approximate functional equation in the theory of the zeta-function with applications to the divisor problem of Dirichlet and Piltz”, Proc. London Math. Soc., 21:2 (1922), 39–74

[9] Voronin S. M., Karatsuba A. A., Dzeta-funktsiya Rimana, Fizmatlit, M., 1994, 376 pp. | MR

[10] Karatsuba A. A., “Approximation of exponential sums by shorter ones”, Proc. Indian Acad. Sci., 97:1–3 (1987), 167–178 | DOI | MR | Zbl

[11] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, 2-e izd., Nauka, M., 1983, 240 pp. | MR

[12] Littlewood J. E., “On the zeros of Riemann zeta-function”, Proc. Camb. Phil. Soc., 22 (1924), 295–318 | DOI | Zbl

[13] Selberg A., “Old and new conjectures and results about a class of Dirichletseries”, Proc. Amalfi Conference on Analytic Number Theory, Univ. Salerno, 1992, 367–386 | MR