On Selberg formulae related to Gram's law
Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1808-1816 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the paper, we obtain a new proof of Selberg formulae related to Gram's law in the theory of the Riemann zeta function. Bibliography: 12 titles.
Keywords: Gram points, Gram's law, Selberg formulae.
@article{SM_2012_203_12_a6,
     author = {M. A. Korolev},
     title = {On {Selberg} formulae related to {Gram's} law},
     journal = {Sbornik. Mathematics},
     pages = {1808--1816},
     year = {2012},
     volume = {203},
     number = {12},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2012_203_12_a6/}
}
TY  - JOUR
AU  - M. A. Korolev
TI  - On Selberg formulae related to Gram's law
JO  - Sbornik. Mathematics
PY  - 2012
SP  - 1808
EP  - 1816
VL  - 203
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/SM_2012_203_12_a6/
LA  - en
ID  - SM_2012_203_12_a6
ER  - 
%0 Journal Article
%A M. A. Korolev
%T On Selberg formulae related to Gram's law
%J Sbornik. Mathematics
%D 2012
%P 1808-1816
%V 203
%N 12
%U http://geodesic.mathdoc.fr/item/SM_2012_203_12_a6/
%G en
%F SM_2012_203_12_a6
M. A. Korolev. On Selberg formulae related to Gram's law. Sbornik. Mathematics, Tome 203 (2012) no. 12, pp. 1808-1816. http://geodesic.mathdoc.fr/item/SM_2012_203_12_a6/

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

[2] H. von Mangoldt, “Zur Verteilung der Nullstellen der Riemannschen Funktion $\gamma(t)$”, Math. Ann., 60:1 (1905), 1–19 | DOI | MR | Zbl

[3] 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 | MR | Zbl

[4] M. A. Korolev, “Gram's law and the argument of the Riemann zeta function”, Publ. Inst. Math. (Beograd), 92:106 (2012) (to appear)

[5] M. Korolev, “On Gram's law in the theory of Riemann zeta function”, Mezhdunarodnaya konferentsiya “Diofantovy priblizheniya. Sovremennoe sostoyanie i prilozheniya” (Minsk, Belarus, 2011), In-t matem. NAN Belarusi, Minsk, 2011, 37–38

[6] M. A. Korolev, “On Gram's law in the theory of the Riemann zeta function”, Izv. Math., 76:2 (2012), 275–309 | DOI | Zbl

[7] A. Selberg, “The zeta-function and the Riemann hypothesis”, C. R. Dixieme Congrès Math. Scandinaves 1946, Jul. Gjellerups Forlag, Copenhagen, 1947, 187–200 | MR | Zbl

[8] J. I. Hutchinson, “On the roots of the Riemann zeta function”, Trans. Amer. Math. Soc., 27:1 (1925), 49–60 | DOI | MR | Zbl

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

[10] A. Fujii, “Gram's law for the zeta zeros and the eigenvalues of Gaussian unitary ensembles”, Proc. Japan Acad. Ser. A Math. Sci., 63:10 (1987), 392–395 | DOI | MR | Zbl

[11] T. Trudgian, “On the success and failure of Gram's law and the Rosser rule”, Acta Arith., 148:3 (2011), 225–256 | DOI | MR | Zbl

[12] A. O. Gel'fond, Calculus of finite differences, Hindustan Publ., Delhi, 1971 | MR | MR | Zbl | Zbl