Geodesic
On small values of the Riemann zeta-function at Gram points
Sbornik. Mathematics, Tome 205 (2014) no. 1, pp. 63-82 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we prove the existence of a large set of Gram points $t_{n}$ such that the values $\zeta(0.5+it_{n})$ are ‘anomalously’ close to zero. A lower bound for the negative ‘discrete’ moment of the Riemann zeta-function on the critical line is also given. Bibliography: 13 titles.
Keywords: Riemann zeta-function, Hardy's function, Gram points. 
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M. A. Korolev. On small values of the Riemann zeta-function at Gram points. Sbornik. Mathematics, Tome 205 (2014) no. 1, pp. 63-82. http://geodesic.mathdoc.fr/item/SM_2014_205_1_a3/

[1] A. A. Karatsuba, S. M. Voronin, The Riemann zeta-function, de Gruyter Exp. Math., 5, Walter de Gruyter Co., Berlin, 1992, xii+396 pp. | MR | MR | Zbl | Zbl

[2] E. C. Titchmarsh, The theory of the Riemann zeta-function, Clarendon Press, Oxford, 1951, vi+346 pp. | MR | Zbl

[3] E. C. Titchmarsh, “The zeros of the Riemann zeta-function”, Proc. R. Soc. Lond. A, 151:873 (1935), 234–255 | DOI | Zbl

[4] J. Kalpokas, J. Steuding, “On the value-distribution of the Riemann zeta-function on the critical line”, Mosc. J. Comb. Number Theory, 1:1 (2011), 26–42 | MR | Zbl

[5] J. Kalpokas, M. A. Korolev, J. Steuding, “Negative values of the Riemann zeta function on the critical line”, Mathematika, 59:2 (2013), 443–462 | DOI | MR | Zbl

[6] A. Selberg, “The zeta-function and the Riemann hypothesis”, C. R. Dixième Congrès Math. Skandinaves 1946, Jul. Gjellerups Forlag, Copenhagen, 1947, 187–200 ; A. Selberg, Collected papers, v. I, Springer-Verlag, Berlin, 1989, 341–355 | MR | Zbl | MR | Zbl

[7] A. Selberg, “Contributions to the theory of the Riemann zeta-function”, Arch. Math. Naturvid., 48:5 (1946), 89–155 ; A. Selberg, Collected papers, v. I, Springer-Verlag, Berlin, 1989, 214–280 | MR | Zbl | MR | Zbl

[8] M. Radziwiłł, Large deviations in Selberg's central limit theorem, 2011, 9 pp., arXiv: 1108. 5092v1

[9] Hsien-Kuei Hwang, “Large deviations for combinatorial distributions. I. Central limit theorems”, Ann. Appl. Probab., 6:1 (1996), 297–319 | DOI | MR | Zbl

[10] M. A. Korolev, “Gram's law and Selberg's conjecture on the distribution of zeros of the Riemann zeta function”, Izv. Math., 74:4 (2010), 743–780 | DOI | DOI | MR | Zbl

[11] Kai-Man Tsang, The distribution of the values of the Riemann zeta-function, Thesis (Ph.D.), Princeton Univ., Princeton, NJ, 1984, 189 pp. | MR

[12] A. A. Karatsuba, M. A. Korolev, “The argument of the Riemann zeta function”, Russian Math. Surveys, 60:3 (2005), 433–488 | DOI | DOI | MR | Zbl

[13] E. Landau, Handbuch der Lehre von der Verteilung der Primzahlen, v. I, B. G. Teubner, Leipzig und Berlin, 1909, xiii + 564 pp. | Zbl