A higher rank Selberg sieve and applications

Akshaa Vatwani

Czechoslovak Mathematical Journal (2018)

  • Volume: 68, Issue: 1, page 169-193
  • ISSN: 0011-4642

Abstract

top
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.

How to cite

top

Vatwani, Akshaa. "A higher rank Selberg sieve and applications." Czechoslovak Mathematical Journal 68.1 (2018): 169-193. <http://eudml.org/doc/294622>.

@article{Vatwani2018,
abstract = {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.},
author = {Vatwani, Akshaa},
journal = {Czechoslovak Mathematical Journal},
keywords = {Selberg sieve; bounded gaps; prime $k$-tuples},
language = {eng},
number = {1},
pages = {169-193},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A higher rank Selberg sieve and applications},
url = {http://eudml.org/doc/294622},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Vatwani, Akshaa
TI - A higher rank Selberg sieve and applications
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 1
SP - 169
EP - 193
AB - 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.
LA - eng
KW - Selberg sieve; bounded gaps; prime $k$-tuples
UR - http://eudml.org/doc/294622
ER -

References

top
  1. Friedlander, J., Iwaniec, H., 10.1090/coll/057, Colloquium Publications, American Mathematical Society 57, Providence (2010). (2010) Zbl1226.11099MR2647984DOI10.1090/coll/057
  2. Halberstam, H., Richert, H.-E., Sieve Methods, London Mathematical Society Monographs 4, Academic Press, London (1974). (1974) Zbl0298.10026MR0424730
  3. Hooley, C., 10.1515/crll.1967.225.209, J. Reine Angew. Math. 225 (1967), 209-220. (1967) Zbl0221.10048MR0207630DOI10.1515/crll.1967.225.209
  4. Lagarias, J. C., Odlyzko, A. M., Effective versions of the Chebotarev density theorem, Algebraic Number Fields: -Functions and Galois Properties Proc. Sympos., Univ. Durham, Durham, 1975, Academic Press, London (1977), 409-464. (1977) Zbl0362.12011MR0447191
  5. Maynard, J., 10.4007/annals.2015.181.1.7, Ann. Math. (2) 181 (2015), 383-413. (2015) Zbl1306.11073MR3272929DOI10.4007/annals.2015.181.1.7
  6. Murty, M. R., Artin's Conjecture and Non-abelian Sieves, Ph.D. Thesis, Massachusetts Institute of Technology, Cambridge (1980). (1980) MR2940944
  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. (1987) Zbl0619.10039MR0894326
  8. Pollack, P., 10.2140/ant.2014.8.1769, Algebra Number Theory 8 (2014), 1769-1786. (2014) Zbl06361769MR3272281DOI10.2140/ant.2014.8.1769
  9. Polymath, D. H. J., 10.1186/s40687-014-0012-7, Res. Math. Sci. (electronic only) 1 (2014), Paper No. 12, 83 pages erratum ibid. (electronic only) 2 2015 Paper No. 15, 2 pages. (2014) Zbl06587992MR3374754DOI10.1186/s40687-014-0012-7
  10. Selberg, A., 10.1090/pspum/020/0567686, 1969 Number Theory Institute Proc. Sympos. Pure Math. 20, Stony Brook, 1969, Amer. Mat. Soc., Providence (1971), 311-351. (1971) Zbl0222.10048MR0567686DOI10.1090/pspum/020/0567686
  11. Selberg, A., Collected Papers. Volume II, Springer, Berlin (1991). (1991) Zbl0729.11001MR1295844
  12. Thorner, J., 10.1186/2197-9847-1-4, Res. Math. Sci. (electronic only) 1 (2014), Paper No. 4, 16 pages. (2014) Zbl06588225MR3344173DOI10.1186/2197-9847-1-4
  13. Vatwani, A., 10.1016/j.jnt.2016.07.008, J. Number Theory 171 (2017), 449-473. (2017) Zbl06643869MR3556693DOI10.1016/j.jnt.2016.07.008
  14. Zhang, Y., 10.4007/annals.2014.179.3.7, Ann. Math. (2) 179 (2014), 1121-1174. (2014) Zbl1290.11128MR3171761DOI10.4007/annals.2014.179.3.7

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.