Geodesic
Theorem on the mean value of $\psi(x,\chi)$ and its applications
Izvestiya. Mathematics, Tome 43 (1994) no. 1, pp. 49-64 
Z. Kh. Rakhmonov. Theorem on the mean value of $\psi(x,\chi)$ and its applications. Izvestiya. Mathematics, Tome 43 (1994) no. 1, pp. 49-64. http://geodesic.mathdoc.fr/item/IM2_1994_43_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new bound for the mean values of Chebyshev functions, taken over all Dirichlet characters, is obtained.

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

[2] Vaughan R. C., “Mean value theorems in prime number theory”, J. London Math. Soc. (2), 10 (1975), 153–162 | DOI | MR | Zbl

[3] Rakhmonov Z. Kh., “Raspredelenie chisel Khardi–Littlvuda v arifmeticheskikh progressiyakh”, Izv. AN SSSR. Ser. matem., 53:1 (1989), 211–224 | MR | Zbl

[4] Karatsuba A. A., “Raspredelenie proizvedenii sdvinutykh prostykh chisel v arifmeticheskikh progressiyakh”, DAN SSSR, 192:4 (1970), 724–727 | Zbl

[5] Vinogradov I. M., Izbrannye trudy, AN SSSR, M., 1952 | MR | Zbl

[6] Vinogradov I. M., Osobye varianty metoda trigonometricheskikh summ, Nauka, M., 1976 | MR

[7] Linnik Yu. V., “Novoe dokazatelstvo teoremy Goldbakha–Vinogradova”, Matem. sb., 19(61):1 (1946), 3–8 | MR | Zbl

[8] Von R., Metod Khardi–Littlvuda, Mir, M., 1985 | MR

[9] Hardy G. H., Wright E. M., An introduction to the theory of numbers, Clareridon Press, Oxford, 1954 | MR | Zbl

[10] Babaev G. B., “Zamechanie k rabote Davenporta i Kheilbrona”, UMN, 13:6(84) (1958), 63–64 | MR | Zbl

[11] Rakhmonov Z. Kh., “O raspredelenii znachenii kharakterov Dirikhle i ikh prilozheniya”, Tr. mezhdunarodnoi konferentsii, posvyaschennoi 100-letiyu I. M. Vinogradova, M., 1991, 317–330

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

[13] Mardzhanishvili K. K., “Otsenka odnoi arifmeticheskoi summy”, DAN SSSR, 22:7 (1939), 391–393

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

[15] Weil A., “On some exponential sams”, Proc. Nat. Acad. S. USA, 34:5 (1948), 204–207 | DOI | MR | Zbl