Geodesic
On the zeros of some Dirichlet series lying on the critical line
Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 55-82.

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

A linear combination of Dirichlet $L$-functions which are known not to have an Euler product is considered. It is proved that the interval $$ \biggl[\frac12-iT,\frac12+iT\biggr] $$ contains for an arbitrary constant $c>0$ more than $cT$ zeros for $T\to\infty$. Bibliography: 9 titles. 
@article{IM2_1981_16_1_a3,
     author = {S. M. Voronin},
     title = {On the zeros of some {Dirichlet} series lying on the critical line},
     journal = {Izvestiya. Mathematics },
     pages = {55--82},
     publisher = {mathdoc},
     volume = {16},
     number = {1},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a3/}
}
TY  - JOUR
AU  - S. M. Voronin
TI  - On the zeros of some Dirichlet series lying on the critical line
JO  - Izvestiya. Mathematics 
PY  - 1981
SP  - 55
EP  - 82
VL  - 16
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a3/
LA  - en
ID  - IM2_1981_16_1_a3
ER  - 
%0 Journal Article
%A S. M. Voronin
%T On the zeros of some Dirichlet series lying on the critical line
%J Izvestiya. Mathematics 
%D 1981
%P 55-82
%V 16
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a3/
%G en
%F IM2_1981_16_1_a3
S. M. Voronin. On the zeros of some Dirichlet series lying on the critical line. Izvestiya. Mathematics , Tome 16 (1981) no. 1, pp. 55-82. http://geodesic.mathdoc.fr/item/IM2_1981_16_1_a3/

[1] Titchmarsh E. K., Teoriya dzeta-funktsii Rimana, M., 1953

[2] Levinson N., “More than on third of zeros of Riemann's zeta-function are on $\sigma= \dfrac 12$”, Adv. Math., 13:4 (1974), 383–436 | DOI | MR | Zbl

[3] Voronin S. M., “O nulyakh dzeta-funktsii kvadratichnykh form”, Tr. Matem. in-ta im. V. A. Steklova AN SSSR, 142, 1976, 135–147 | MR | Zbl

[4] Siegel C. L., “Contributions to the theory of the Dirichlet $L$-series and the Epstein zeta-functions”, Ann. Mathematics, 44:2 (1943), 123–151 | MR

[5] Davenport G., Multiplikativnaya teoriya chisel, Nauka, M., 1971 | MR | Zbl

[6] Landau E., Handbuch der Lehre von der Verteilung Primzahlen. I, Leipzig, 1909

[7] Chulanovskii I. V., “Nekotorye otsenki, svyazannye s novym metodom Selberg'a v elementarnoi teorii chisel”, Dokl. AN SSSR, 63 (1948), 491–494

[8] Montgomeri G., Multiplikativnaya teoriya chisel, Mir, M., 1974 | MR

[9] Kassels Dzh. V. S., Vvedenie v teoriyu diofantovykh priblizhenii, Mir, M., 1961