Geodesic
On Karatsuba's problem related to Gram's law
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 162-172.

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

A number of new results related to Gram's law in the theory of the Riemann zeta-function are proved. In particular, a lower bound is obtained for the number of ordinates of the zeros of the zeta-function that lie in a given interval and satisfy Gram's law. 
@article{TM_2012_276_a12,
     author = {M. A. Korolev},
     title = {On {Karatsuba's} problem related to {Gram's} law},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {162--172},
     publisher = {mathdoc},
     volume = {276},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2012_276_a12/}
}
TY  - JOUR
AU  - M. A. Korolev
TI  - On Karatsuba's problem related to Gram's law
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2012
SP  - 162
EP  - 172
VL  - 276
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2012_276_a12/
LA  - ru
ID  - TM_2012_276_a12
ER  - 
%0 Journal Article
%A M. A. Korolev
%T On Karatsuba's problem related to Gram's law
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2012
%P 162-172
%V 276
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2012_276_a12/
%G ru
%F TM_2012_276_a12
M. A. Korolev. On Karatsuba's problem related to Gram's law. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Number theory, algebra, and analysis, Tome 276 (2012), pp. 162-172. http://geodesic.mathdoc.fr/item/TM_2012_276_a12/

[1] Gourdon X., Computation of zeros of the zeta function, , 2004 http://numbers.computation.free.fr/Constants/Miscellaneous/zetazeroscompute.html

[2] Gram J.-P., “Note sur les zéros de la fonction $\zeta (s)$ de Riemann”, Acta math., 27 (1903), 289–304 | DOI | MR | Zbl

[3] Korolev M.A., Gram's law and the argument of the Riemann zeta function, E-print, 2011, arXiv: 1106.0516v2 [math.NT] | MR

[4] Selberg A., “The zeta-function and the Riemann hypothesis”, 10. Skand. Mat. Kongr., København, 1946, Jul. Gjellerups Forlag, Copenhagen, 1947, 187–200 | MR

[5] Selberg A., Collected papers, V. 1, Springer, Berlin, 1989 | MR | Zbl

[6] Korolëv M.A., “Zakon Grama i gipoteza Selberga o raspredelenii nulei dzeta-funktsii Rimana”, Izv. RAN. Ser. mat., 74:4 (2010), 83–118 | DOI | MR | Zbl

[7] Korolev M.A., On the Gram's law in the theory of Riemann zeta function, E-print, 2010, arXiv: 1011.3997v1 [math.NT] | MR

[8] Selberg A., “On the remainder in the formula for $N(T)$, the number of zeros of $\zeta (s)$ in the strip $0$”, Avh. Norske Vid. Akad. Oslo. I: Mat.-Naturv. Kl., 1944, no. 1, 1–27 | MR | Zbl

[9] Selberg A., “Contributions to the theory of the Riemann zeta-function”, Arch. Math. Naturv., 48:5 (1946), 89–155 | MR | Zbl

[10] Karatsuba A.A., Korolëv M.A., “Povedenie argumenta dzeta-funktsii Rimana na kriticheskoi pryamoi”, UMN, 61:3 (2006), 3–92 | DOI | MR | Zbl

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

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

[13] Karatsuba A.A., Korolëv M.A., “Argument dzeta-funktsii Rimana”, UMN, 60:3 (2005), 41–96 | DOI | MR | Zbl

[14] Korolëv M.A., “O bolshikh znacheniyakh funktsii $S(t)$ na korotkikh promezhutkakh”, Izv. RAN. Ser. mat., 69:1 (2005), 115–124 | DOI | MR | Zbl

[15] Titchmarsh E.K., Teoriya dzeta-funktsii Rimana, Izd-vo inostr. lit., M., 1953

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

[17] Boyarinov R.N., “Argument dzeta-funktsii Rimana”, Chebyshev. sb., 11:1 (2010), 54–67 | MR | Zbl

[18] Tsang K.-M., The distribution of the values of the Riemann zeta-function, PhD Diss., Princeton Univ., Princeton, 1984 | MR