Zeros of a~special type of function associated with Hecke $L$-functions of imaginary quadratic fields
Izvestiya. Mathematics , Tome 61 (1997) no. 1, pp. 45-68.

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

We obtain a bound for the number of zeros on the interval $[T,2T]$ of a linear combination of a special type of real-valued function associated with the Hecke $L$-functions of a fixed imaginary quadratic field corresponding to complex characters.
@article{IM2_1997_61_1_a1,
     author = {S. A. Gritsenko},
     title = {Zeros of a~special type of function associated with {Hecke} $L$-functions of imaginary quadratic fields},
     journal = {Izvestiya. Mathematics },
     pages = {45--68},
     publisher = {mathdoc},
     volume = {61},
     number = {1},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a1/}
}
TY  - JOUR
AU  - S. A. Gritsenko
TI  - Zeros of a~special type of function associated with Hecke $L$-functions of imaginary quadratic fields
JO  - Izvestiya. Mathematics 
PY  - 1997
SP  - 45
EP  - 68
VL  - 61
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a1/
LA  - en
ID  - IM2_1997_61_1_a1
ER  - 
%0 Journal Article
%A S. A. Gritsenko
%T Zeros of a~special type of function associated with Hecke $L$-functions of imaginary quadratic fields
%J Izvestiya. Mathematics 
%D 1997
%P 45-68
%V 61
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a1/
%G en
%F IM2_1997_61_1_a1
S. A. Gritsenko. Zeros of a~special type of function associated with Hecke $L$-functions of imaginary quadratic fields. Izvestiya. Mathematics , Tome 61 (1997) no. 1, pp. 45-68. http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a1/

[1] Selberg A., “Old and new conjectures and results about a class of Dirichlet series”, Proc. of the Amalfi conference on Analytic Number Theory, Univ. di. Salerno, 1992, 365–387 | MR

[2] Conrey J. B., Ghosh A., “On the Selberg class of Dirichlet series: small degrees”, Duke Math. J., 72:3 (1993), 673–695 | DOI | MR

[3] Karatsuba A. A., “Novyi podkhod k probleme nulei nekotorykh ryadov Dirikhle”, Tr. MIRAN, 207 (1994), 180–196 | MR | Zbl

[4] Karatsuba A. A., “Nuli arifmeticheskikh nulei Dirikhle”, Math. Slovaca, 44:5 (1994), 633–649 | MR | Zbl

[5] Bombieri E., Hejhal D., “Sur les zéros des fonctions zêta d'Epstein”, C. R. Acad. Sci. Paris. Ser. I. Math., 304 (1987), 213–217 | MR | Zbl

[6] Hejhal D., “Zeros of Epstein zeta-functions and Supercomputers”, Proc. Intern. Congr. Math. Berkeley (Calif., USA), 1986, 1362–1383 | MR

[7] Davenport H., Heilbronn H., “On the zeros of certain Dirichlet series”, J. Lond. Math. Soc., 11 (1936), 181–185 ; 307–312 | DOI | Zbl | Zbl

[8] Karatsuba A. A., “O nulyakh funktsii Devenporta–Kheilbronna, lezhaschikh na kriticheskoi pryamoi”, Izv. AN SSSR. Ser. matem., 54:2 (1990), 303–315 | MR | Zbl

[9] Voronin S. M., “O nulyakh dzeta-funktsii kvadratichnykh form”, Tr. MIAN, 142, Nauka, M., 1976, 135–147 | MR | Zbl

[10] Voronin S. M., “O nulyakh dzeta-funktsii kvadratichnykh form”, DAN SSSR, 235:2 (1977), 257–258 | MR | Zbl

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

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

[13] Hardy G., Littlewood J. E., “The zeros of Riemann zeta-function on the critical line”, Math. Zs., 10 (1921), 283–317 | DOI | MR | Zbl

[14] Voronin S. M., “O nulyakh nekotorykh ryadov Dirikhle, lezhaschikh na kriticheskoi pryamoi”, Izv. AN SSSR. Ser. matem., 44:1 (1980), 63–91 | MR | Zbl

[15] Karatsuba A. A., “O nulyakh funktsii Devenporta–Kheilbronna, lezhaschikh na kriticheskoi pryamoi”, Izv. AN SSSR. Ser. matem., 54:2 (1990), 303–315 | MR | Zbl

[16] Karatsuba A. A., “O nulyakh spetsialnogo vida funktsii, svyazannykh s ryadami Dirikhle”, Izv. AN SSSR. Ser. matem., 55:3 (1991), 483–514

[17] Gritsenko S. A., “O nulyakh lineinykh kombinitsii spetsialnogo vida funktsii, svyazannykh s ryadami Dirikhle iz klassa Selberga”, Izv. RAN. Ser. matem., 60:4 (1996), 3–42 | MR | Zbl

[18] Aierlend K., Rouzen M., Klassicheskoe vvedenie v sovremennuyu teoriyu chisel, Mir, M., 1987 | MR

[19] Leng S., Algebraicheskie chisla, Mir, M., 1966 | MR

[20] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1973

[21] Lavrik A. F., “Priblizhennoe funktsionalnoe uravnenie dzeta-funktsii Gekke mnimogo kvadratichnogo polya”, Matem. zametki, 2:5 (1967), 475–482 | MR | Zbl

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

[23] Prakhar K., Raspredelenie prostykh chisel, Mir, M., 1967 | MR