Geodesic
The argument of the Riemann zeta-function on the critical line
Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 225-264.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove a new density theorem for the zeros of the Riemann zeta-function in the critical strip, and apply it to the problem of the number of sign changes of the argument of the zeta-function on almost all short intervals of the critical line. 
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M. A. Korolev. The argument of the Riemann zeta-function on the critical line. Izvestiya. Mathematics , Tome 67 (2003) no. 2, pp. 225-264. http://geodesic.mathdoc.fr/item/IM2_2003_67_2_a2/

[1] Selberg A., “Contributions to the theory of the Riemann zeta-function”, Archiv for Mathematik og Naturvidenskab., 48:5 (1946), 89–155 | MR | Zbl

[2] Titchmarsh E. C., “The zeros of the Riemann zeta-function”, Proc. Royal Soc., 151 (1935), 234–255 | DOI | Zbl

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

[4] Ghosh A., “On Riemann's Zeta-Function – Sign Changes of $S(T)$”, Recent Progress in Analytic Number Theory, V. 1, Academic Press, N. Y., 1981, 29–46 | MR

[5] Karatsuba A. A., “O funktsii $S(t)$”, Izv. RAN. Ser. matem., 60:5 (1996), 27–56 | MR | Zbl

[6] Karatsuba A. A., “Plotnostnaya teorema i povedenie argumenta dzeta-funktsii Rimana”, Matem. zametki, 60:3 (1996), 448–449 | MR | Zbl

[7] Korolëv M. A., “O chisle peremen znaka funktsii $S(t)$ na korotkom promezhutke”, Dokl. RAN, 382:4 (2002), 446–447 | MR

[8] Mueller J., “On the Riemann zeta-function $\zeta(s)$ – gaps between sign changes of $S(t)$”, Mathematika, 29:2 (1982), 264–269 | MR | Zbl

[9] Selberg A., “Old and New Conjectures and Results About a Class of Dirichlet Series”, Proc. of the Amalfi conference, Univ. Di Salerno, 1992, 365–387 | MR

[10] Karatsuba A. A., “Raspredelenie nulei funktsii $\zeta\bigl(\frac{1}{2}+it\bigr)$”, Izv. AN SSSR. Ser. matem., 48:6 (1984), 1214–1222 | MR

[11] 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

[12] 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

[13] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, 1-e izd., Nauka, M., 1975 | MR | Zbl

[14] 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. Acad. Mat.-Nat. Kl. 1, 1944 | MR

[15] Postnikov A. G., Ergodicheskie voprosy teorii sravnenii i teorii diofantovykh priblizhenii, Tr. matem. in-ta im. V. A. Steklova AN SSSR, 82, 1966 | MR | Zbl

[16] Kats M., Statisticheskaya nezavisimost v teorii veroyatnostei, analize i teorii chisel, IL, M., 1963

[17] Ghosh A., “On the Riemann zeta-function-mean value theorems and the distribution of $|S(t)|$”, J. of Number Theory, 17 (1983), 93–102 | DOI | MR | Zbl

[18] Tsang K.-M., “Some $\Omega$-theorems for the Riemann zeta-function”, Acta Arithmetica, 46:4 (1986), 369–395 | MR | Zbl