Geodesic
On the zeros of arithmetic Dirichlet series without Euler product
Izvestiya. Mathematics , Tome 43 (1994) no. 2, pp. 193-203.

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A perfected version is proposed of the author's method for finding a lower bound for the number of zeros of combinations of Dirichlet functions that lie on intervals of the critical line. 
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A. A. Karatsuba. On the zeros of arithmetic Dirichlet series without Euler product. Izvestiya. Mathematics , Tome 43 (1994) no. 2, pp. 193-203. http://geodesic.mathdoc.fr/item/IM2_1994_43_2_a0/

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

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

[3] Karatsuba A. A., “O nulyakh nekotorykh ryadov Dirikhle”, UMN, 45:1(271) (1990), 175–176 | MR | Zbl

[4] Karatsuba A. A., “Utochnenie teorem o kolichestve nulei, lezhaschikh na kriticheskoi pryamoi, nekotorykh ryadov Dirikhle”, UMN, 47:2(284) (1992), 193–194 | MR | Zbl

[5] Karatsuba A. A., “O kolichestve nulei dzeta-funktsii Rimana, lezhaschikh na pochti vsekh korotkikh promezhutkakh kriticheskoi pryamoi”, Izv. AN SSSR. Ser. matem., 56:2 (1992), 372–397 | MR

[6] Karatsuba A. A., Voronin S. M., The Riemann Zeta-Function, W. de G., Berlin, N.Y., 1992 | MR

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

[8] Karatsuba A. A., Dzeta-funktsiya Rimana i ee nuli, UMN, 40, no. 5(245), 1985 | MR | Zbl