The Hua Loo-Keng problem on prime~numbers representable
Izvestiya. Mathematics , Tome 71 (2007) no. 3, pp. 477-493.

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In this paper, we solve the Hua Loo-Keng problem with prime numbers representable by given primitive positive-definite binary quadratic forms whose discriminants coincide with those of the imaginary quadratic fields in which the quadratic forms decompose into linear factors.
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S. A. Gritsenko. The Hua Loo-Keng problem on prime~numbers representable. Izvestiya. Mathematics , Tome 71 (2007) no. 3, pp. 477-493. http://geodesic.mathdoc.fr/item/IM2_2007_71_3_a3/

[1] Lo-ken Khua, Additivnaya teoriya prostykh chisel, Tr. MIAN, 22, 1947 ; Loo-keng Hua, Additive theory of prime numbers, Transl. Math. Monogr., 13, Amer. Math. Soc., Providence, RI, 1965 | MR | Zbl | MR | Zbl

[2] Z. I. Borevich, I. R. Shafarevich, Teoriya chisel, Nauka, M., 1985 ; Z. I. Borevich, I. R. Shafarevich, Number theory, Pure Appl. Math., 20, Academic Press, New York–London, 1966 | MR | Zbl | MR | Zbl

[3] E. Gekke, Lektsii po teorii algebraicheskikh chisel, GITTL, M.–L., 1940; E. Hecke, Vorlesungen über die Theorie der algebraischen Zahlen, Akad. Verlagsges, Leipzig, 1923 | MR | Zbl

[4] K. F. Aierlend, M. I. Rouzen, Klassicheskoe vvedenie v sovremennuyu teoriyu chisel, Mir, M., 1987 ; K. F. Ireland, M. I. Rosen, A classical introduction to modern number theory, Grad. Texts in Math., 84, Springer-Verlag, New York–Heidelberg–Berlin, 1982 | MR | Zbl | MR | Zbl

[5] S. A. Gritsenko, “O funktsionalnom uravnenii odnogo arifmeticheskogo ryada Dirikhle”, Tr. V Mezhdunarodnoi konferentsii “Algebra i teoriya chisel: sovremennye problemy i prilozheniya” (Rossiya, Tula, 2003), Chebyshevskii sb., 4:2(6) (2003), 55–67 | MR | Zbl

[6] S. A. Gritsenko, “O raspredelenii norm prostykh idealov iz zadannogo klassa v arifmeticheskikh progressiyakh”, Zapiski nauch. sem. POMI, 322 (2005), 45–62 | MR | Zbl

[7] Loo Keng Hua, Introduction to number theory, Springer-Verlag, Berlin–Heidelberg–New York, 1982 | MR | Zbl

[8] S. M. Voronin, A. A. Karatsuba, Dzeta-funktsiya Rimana, Fizmatlit, M., 1994 ; S. M. Voronin, A. A. Karatsuba, The Riemann zeta-function, de Gruyter Exp. Math., 5, Walter de Gruyter and Co., Berlin, 1992 | MR | Zbl | MR | Zbl

[9] A. A. Karatsuba, Osnovy analiticheskoi teorii chisel, Nauka, M., 1983 ; A. A. Karatsuba, Basic analytic number theory, Springer-Verlag, Berlin, 1993 | MR | Zbl | MR | Zbl

[10] I. M. Vinogradov, Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1980 ; I. M. Vinogradov, The method of trigonometrical sums in the theory of numbers, Dover Publ., Inc., Mineola, NY, 2004 | MR | Zbl | MR | Zbl