Geodesic
Zeros of the derivatives of the Riemann $\xi$-function
Izvestiya. Mathematics , Tome 69 (2005) no. 3, pp. 539-605.

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

We show that the proportion of the zeros of the $k$th derivative of the Riemann $\xi$-function (where $k\geqslant1$ is an integer) that are on the critical line is greater than $1-\frac{3}{5}\,k^{-2}$. 
@article{IM2_2005_69_3_a3,
     author = {I. S. Rezvyakova},
     title = {Zeros of the derivatives of the {Riemann} $\xi$-function},
     journal = {Izvestiya. Mathematics },
     pages = {539--605},
     publisher = {mathdoc},
     volume = {69},
     number = {3},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2005_69_3_a3/}
}
TY  - JOUR
AU  - I. S. Rezvyakova
TI  - Zeros of the derivatives of the Riemann $\xi$-function
JO  - Izvestiya. Mathematics 
PY  - 2005
SP  - 539
EP  - 605
VL  - 69
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2005_69_3_a3/
LA  - en
ID  - IM2_2005_69_3_a3
ER  - 
%0 Journal Article
%A I. S. Rezvyakova
%T Zeros of the derivatives of the Riemann $\xi$-function
%J Izvestiya. Mathematics 
%D 2005
%P 539-605
%V 69
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2005_69_3_a3/
%G en
%F IM2_2005_69_3_a3
I. S. Rezvyakova. Zeros of the derivatives of the Riemann $\xi$-function. Izvestiya. Mathematics , Tome 69 (2005) no. 3, pp. 539-605. http://geodesic.mathdoc.fr/item/IM2_2005_69_3_a3/

[1] Hardy G. H., “Sur les zeros de la fonction $\zeta(s)$ de Riemann”, Compt. Rend. Acad. Sci., 158 (1914), 1012–1014 | Zbl

[2] Selberg A., “On the zeros of Riemann's zeta-function”, Skr. Norske Vid. Akad. Oslo, 10 (1942), 1–59 | MR

[3] Levinson N., “More than one-third of zeros of Riemann's zeta-function are on $\sigma = 1/2$”, Adv. in Math., 13 (1974), 383–436 | DOI | MR | Zbl

[4] Conrey B., “Zeros of derivatives of Riemann's $\xi$-function on the critical line”, J. of Number Theory, 16 (1983), 49–74 | DOI | MR | Zbl

[5] Conrey B., “More than $2/5$ of the zeros of the Riemann's zeta-function are on the critical line”, J. Reine Angew. Math., 399 (1989), 1–26 | MR | Zbl

[6] Siegel C. L., “Über Riemanns Nachlaß zur analytischen Zahlentheorie”, Quellen Stud. Geschichte Math. Astronom. Phys. Abt. B. Stud. 2, 1932, 45–80

[7] Karatsuba A. A., “O rasstoyanii mezhdu sosednimi nulyami dzeta-funktsii Rimana, lezhaschimi na kriticheskoi pryamoi”, Tr. MIAN, 157, Nauka, M., 1981, 49–63 | MR | Zbl

[8] Lavrik A. A., “Ravnomernye priblizheniya i nuli v korotkikh intervalakh proizvodnykh $Z$-funktsii Khardi”, Anal. Math., 17 (1991), 257–279 | DOI | MR | Zbl

[9] Voronin S. M., Karatsuba A. A., Dzeta-funktsiya Rimana, Fizmatlit, M., 1994 | MR

[10] Titchmarsh E. K., Teoriya funktsii, Per. s angl. 2-e izd., pererab., Nauka, M., 1980 | MR | Zbl

[11] Titchmarsh E. C., The theory of the Riemann Zeta-function, 2nd ed., ed. D. R. Heath-Brown, Oxford University Press, N. Y.–Oxford, 2001, 412 pp. | MR