Geodesic
Three additive problems
Izvestiya. Mathematics , Tome 41 (1993) no. 3, pp. 447-464.

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

Variants of two classical additive problems – the ternary Goldbach problem and the Goldbach–Waring problem – are solved in prime numbers lying in intervals of a special form. A binary additive problem with numbers in the sequence $[n^c]$, $c>1$, is also solved. 
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S. A. Gritsenko. Three additive problems. Izvestiya. Mathematics , Tome 41 (1993) no. 3, pp. 447-464. http://geodesic.mathdoc.fr/item/IM2_1993_41_3_a2/

[1] Vinogradov I. M., “Nekotoroe obschee svoistvo raspredeleniya prostykh chisel”, Matem. sb., 7 (1940), 365–372 | Zbl

[2] Gritsenko S. A., “Ob odnoi zadache I. M. Vinogradova”, Matem. zametki, 39:5 (1986), 625–640 | MR | Zbl

[3] Gritsenko S. A., “Ternarnaya problema Goldbakha i problema Goldbakha–Varinga s prostymi chislami, lezhaschimi v promezhutkakh spetsialnogo vida”, UMN, 43:4(262) (1988), 203–204 | MR

[4] Vaughan R., “On the distribution of $\alpha p$ modulo 1”, Mathematica, 24:48 (1979), 135–141 | MR

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

[6] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1980 | MR

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

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

[9] Deshouillers J. M., “Un problème binaire en théorie additive”, Acta Arithmetica, XXV (1974), 393–403 | MR

[10] Pyatetskii-Shapiro I. I., “O raspredelenii prostykh chisel v posledovatelnosti $[n^c]$”, Matem. sb., 33:3 (1953), 559–566