Geodesic
A remark on the distribution of the zeros of Riemann's zeta function
Sbornik. Mathematics, Tome 194 (2003) no. 10, pp. 1533-1542 
A. V. Egorov. A remark on the distribution of the zeros of Riemann's zeta function. Sbornik. Mathematics, Tome 194 (2003) no. 10, pp. 1533-1542. http://geodesic.mathdoc.fr/item/SM_2003_194_10_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A certain new symmetric representation of Riemann's xi function is considered. A theorem on the zeros of trigonometric integrals analogous to Kakeya's theorem on the zeros of polynomials with monotonically non-decreasing coefficients is used. A modification of Polya's method is suggested, which allows one to obtain new assertions on the disposition of the zeros of the zeta function.

[1] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, Nauka, M., 1983 | MR

[2] Edwards H. M., Riemann's zeta function, Academic Press, New York, 1974 | MR | Zbl

[3] Kakeya S., “On the limits of the roots of an algebraic equation with positive coefficients”, Tôhoku Math. J., 2:3 (1912)

[4] Pólya G., “Über die Nullstellen gewisser ganzer Funktionen”, Math. Z., 2 (1918), 352–383 | DOI | MR | Zbl