Geodesic
Zeros of linear combinations of functions of a~special type that are connected with Selberg Dirichlet series
Izvestiya. Mathematics , Tome 60 (1996) no. 4, pp. 655-694.

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Assuming that a conjecture of Selberg holds, along with certain other conditions, we obtain a lower bound on an interval of the critical line for the number of zeros of a function that is a linear combination of the analogues of the Riemann zeta-function that correspond to Dirichlet series of the Selberg class. 
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S. A. Gritsenko. Zeros of linear combinations of functions of a~special type that are connected with Selberg Dirichlet series. Izvestiya. Mathematics , Tome 60 (1996) no. 4, pp. 655-694. http://geodesic.mathdoc.fr/item/IM2_1996_60_4_a0/

[1] Selberg A., “Old and new conjectures and results about a class of Dirichlet series”, Proc. of the Amalfi Conf. on Anal. Number Theory, Univ. di Salerno, 1992, 367–385 | MR | Zbl

[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 ryadov 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, 1362–1384 | MR

[7] Davenport H., Heilbronn H., “On the zeros of certain Dirichlet series”, J. London Math. Soc., 11 (1936), 181–185, 307–312 | DOI | 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] Hardy G. H., Littlewood J. E., “The zeros of Riemann zeta-function on the critical line”, Math. Zs., 10 (1921), 283–317 | DOI | MR | Zbl

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

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

[14] Lavrik A. A., “Problema Titchmarsha diskretnoi teorii dzeta-funktsii Rimana”, Tr. MIRAN, 207 (1994), 197–230 | MR | Zbl

[15] Iviĉ A., The Riemann zeta-function, John Wiley and Sons, N. Y., 1985 | MR | Zbl

[16] Hardy G. H., Wright E. M., An introduction to the Theory of Numbers, 4-th edition, Clarendon Press, Oxford, 1959 | MR

[17] Khooli K., Primenenie metodov resheta v teorii chisel, Nauka, M., 1987 | MR