Geodesic
Bounded gaps between primes of special form
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 75-78.

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

Let $0\alpha$, $\sigma1$ be arbitrary fixed constants, let $q_1$ be the set of primes satisfying the condition $\{q_n^\alpha\}\sigma$ and indexed in ascending order, and let $m\ge1$ be any fixed integer. Using an analogue of the Bombieri–Vinogradov theorem for the above set of primes, upper bounds are obtained for the constants $c(m)$ such that the inequality $q_{n+m}-q_n\le c(m)$ holds for infinitely many $n$.
Keywords: consecutive primes, small gaps, fractional parts, bounded gaps, sieve method, Bombieri–Vinogradov theorem. 
@article{DANMA_2020_492_a15,
     author = {A. V. Shubin},
     title = {Bounded gaps between primes of special form},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {75--78},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_492_a15/}
}
TY  - JOUR
AU  - A. V. Shubin
TI  - Bounded gaps between primes of special form
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 75
EP  - 78
VL  - 492
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_492_a15/
LA  - ru
ID  - DANMA_2020_492_a15
ER  - 
%0 Journal Article
%A A. V. Shubin
%T Bounded gaps between primes of special form
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 75-78
%V 492
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2020_492_a15/
%G ru
%F DANMA_2020_492_a15
A. V. Shubin. Bounded gaps between primes of special form. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 75-78. http://geodesic.mathdoc.fr/item/DANMA_2020_492_a15/

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

[2] Vinogradov I.M., “Otsenka odnoi trigonometricheskoi summy po prostym chislam”, Izv. AN SSSR. Ser. matem., 23:2 (1959), 157–164 | Zbl

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

[4] Linnik Yu.V., “Ob odnoi teoreme teorii prostykh chisel”, DAN SSSR, 47:1 (1945), 7–8

[5] Kaufman R.M., “O raspredelenii $\{ \sqrt p \} $”, Matem. zametki, 26:4 (1979), 497–504 | MR | Zbl

[6] Benatar J., “The Existence of Small Prime Gaps in Subsets of the Integers”, Int. J. Number Theory, 11:3 (2015), 801–833 | DOI | MR | Zbl

[7] Maynard J., “Dense Clusters of Primes in Subsets”, Compos. Math., 152:7 (2016), 1517–1554 | DOI | MR | Zbl

[8] Tolev D.I., “On a Theorem of Bombieri-Vinogradov Type for Prime Numbers from a Thin Set”, Acta Arith., 81:1 (1997), 57–68 | DOI | MR | Zbl

[9] Gritsenko S.A., Zinchenko N.A., “Ob otsenke odnoi trigonometricheskoi summy po prostym chislam”, Nauchnye vedomosti Belgorodskogo gos. un-ta. Seriya: Matematika. Fizika, 5 (148):30 (2013), 48–52

[10] Maynard J., “Small Gaps between Primes”, Ann. Math., 181:1 (2015), 383–413 | DOI | MR | Zbl