Geodesic
Primes in Special Intervals and Additive Problems with Such Numbers
Matematičeskie zametki, Tome 73 (2003) no. 3, pp. 423-436.

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We study primes in a special set $E$ which is naturally described by the fractional part of $p^a$, where $a1$ is a noninteger. An asymptotic formula with power lowering in the remainder of the trigonometric sum over primes from the set $E$ is obtained. We study several applications of this result to problems of the distribution of primes from $E$ in arithmetic progressions and to additive problems with primes from $E$. 
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M. E. Changa. Primes in Special Intervals and Additive Problems with Such Numbers. Matematičeskie zametki, Tome 73 (2003) no. 3, pp. 423-436. http://geodesic.mathdoc.fr/item/MZM_2003_73_3_a8/

[1] Vinogradov I. M., “Nekotoroe obschee svoistvo raspredeleniya prostykh chisel”, Matem. sb., 7 (49):2 (1940), 365–372 | MR | Zbl

[2] Vinogradov I. M., Osobye varianty metoda trigonometricheskikh summ, Nauka, M., 1976

[3] Linnik Yu. V., “Ob odnoi teoreme teorii prostykh chisel”, Dokl. AN SSSR, 47:1 (1945), 7–8 | MR

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

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

[6] Vinogradov I. M., “Otsenka odnoi trigonometricheskoi summy po prostym chislam”, Izv. AN SSSR. Ser. matem., 23 (1959), 157–164 | MR | Zbl

[7] Leitmann D., “On the uniform distribution of some sequences”, J. London Math. Soc. (2), 14:3 (1976), 430–432 | DOI | MR | Zbl

[8] Baker R. C., Kolesnik G., “On the distribution of $p^\alpha$ modulo one”, J. Reine Angew. Math., 356 (1985), 174–193 | MR | Zbl

[9] Cao X., Zhai W., “On the distribution of $p^\alpha$ modulo one”, J. Théor. Nombres Bordeaux, 11:2 (1999), 407–423 | MR | Zbl

[10] Vinogradov I. M., Metod trigonometricheskikh summ v teorii chisel, Nauka, M., 1980

[11] Karatsuba A. A., Osnovy analiticheskoi teorii chisel, Nauka, M., 1983

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

[13] Khua L.-K., Additivnaya teoriya prostykh chisel, Tr. MIAN, 22, Nauka, M.–L., 1947 | MR | Zbl

[14] Estermann T., “Proof that every large integer is the sum of two primes and a square”, Proc. London Math. Soc. Ser. 2, 42 (1937), 501–516 | DOI | Zbl