Geodesic
A higher rank Selberg sieve and applications
Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 169-193 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.
We develop an axiomatic formulation of the higher rank version of the classical Selberg sieve. This allows us to derive a simplified proof of the Zhang and Maynard-Tao result on bounded gaps between primes. We also apply the sieve to other subsequences of the primes and obtain bounded gaps in various settings.
DOI : 10.21136/CMJ.2017.0410-16
Classification : 11N05, 11N35, 11N36
Keywords: Selberg sieve; bounded gaps; prime $k$-tuples 
@article{10_21136_CMJ_2017_0410_16,
     author = {Vatwani, Akshaa},
     title = {A higher rank {Selberg} sieve and applications},
     journal = {Czechoslovak Mathematical Journal},
     pages = {169--193},
     year = {2018},
     volume = {68},
     number = {1},
     doi = {10.21136/CMJ.2017.0410-16},
     mrnumber = {3783592},
     zbl = {06861574},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0410-16/}
}
TY  - JOUR
AU  - Vatwani, Akshaa
TI  - A higher rank Selberg sieve and applications
JO  - Czechoslovak Mathematical Journal
PY  - 2018
SP  - 169
EP  - 193
VL  - 68
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0410-16/
DO  - 10.21136/CMJ.2017.0410-16
LA  - en
ID  - 10_21136_CMJ_2017_0410_16
ER  - 
%0 Journal Article
%A Vatwani, Akshaa
%T A higher rank Selberg sieve and applications
%J Czechoslovak Mathematical Journal
%D 2018
%P 169-193
%V 68
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2017.0410-16/
%R 10.21136/CMJ.2017.0410-16
%G en
%F 10_21136_CMJ_2017_0410_16
Vatwani, Akshaa. A higher rank Selberg sieve and applications. Czechoslovak Mathematical Journal, Tome 68 (2018) no. 1, pp. 169-193. doi: 10.21136/CMJ.2017.0410-16

[1] Friedlander, J., Iwaniec, H.: Opera de Cribro. Colloquium Publications, American Mathematical Society 57, Providence (2010). | DOI | MR | JFM

[2] Halberstam, H., Richert, H.-E.: Sieve Methods. London Mathematical Society Monographs 4, Academic Press, London (1974). | MR | JFM

[3] Hooley, C.: On Artin's conjecture. J. Reine Angew. Math. 225 (1967), 209-220. | DOI | MR | JFM

[4] Lagarias, J. C., Odlyzko, A. M.: Effective versions of the Chebotarev density theorem. Algebraic Number Fields: $L$-Functions and Galois Properties Proc. Sympos., Univ. Durham, Durham, 1975, Academic Press, London (1977), 409-464. | MR | JFM

[5] Maynard, J.: Small gaps between primes. Ann. Math. (2) 181 (2015), 383-413. | DOI | MR | JFM

[6] Murty, M. R.: Artin's Conjecture and Non-abelian Sieves. Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge (1980). | MR

[7] Murty, M. R., Murty, V. K.: A variant of the Bombieri-Vinogradov theorem. Number Theory Proc. Conf., Montreal, 1985, CMS Conf. Proc. 7 (1987), 243-272. | MR | JFM

[8] Pollack, P.: Bounded gaps between primes with a given primitive root. Algebra Number Theory 8 (2014), 1769-1786. | DOI | MR | JFM

[9] Polymath, D. H. J.: Variants of the Selberg sieve, and bounded intervals containing many primes. Res. Math. Sci. (electronic only) 1 (2014), Paper No. 12, 83 pages erratum ibid. (electronic only) 2 2015 Paper No. 15, 2 pages. | DOI | MR | JFM

[10] Selberg, A.: Sieve methods. 1969 Number Theory Institute Proc. Sympos. Pure Math. 20, Stony Brook, 1969, Amer. Mat. Soc., Providence (1971), 311-351. | DOI | MR | JFM

[11] Selberg, A.: Collected Papers. Volume II. Springer, Berlin (1991). | MR | JFM

[12] Thorner, J.: Bounded gaps between primes in Chebotarev sets. Res. Math. Sci. (electronic only) 1 (2014), Paper No. 4, 16 pages. | DOI | MR | JFM

[13] Vatwani, A.: Bounded gaps between Gaussian primes. J. Number Theory 171 (2017), 449-473. | DOI | MR | JFM

[14] Zhang, Y.: Bounded gaps between primes. Ann. Math. (2) 179 (2014), 1121-1174. | DOI | MR | JFM

Cité par Sources :