Article

Access to the text (HTML) Access to the text (HTML)
PDF Access to the PDF text
Advertising


Access to the full text of this article requires a subscription.
  • If you are a subscriber, please sign in 'My Account' at the top right of the screen.

  • If you want to subscribe to this journal, see our rates

  • You can purchase this item in Pay Per ViewPay per View - FAQ : 30,00 € Taxes included to order
    Pages Iconography Videos Other
    5 0 0 0


Comptes Rendus Mathématique
Volume 343, n° 3
pages 155-159 (août 2006)
Doi : 10.1016/j.crma.2006.05.023
Received : 29 May 2006 ; 
Sieving and expanders
Cribles et expanseurs
 

Jean Bourgain a , Alex Gamburd a, b , Peter Sarnak a, c
a School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA 
b Department of Mathematics, University of California, Santa Cruz, USA 
c Department of Mathematics, Princeton University, USA 

Abstract

Let V be an orbit in   of a finitely generated subgroup of   whose Zariski closure   is suitably large (e.g. isomorphic to  ). We develop a Brun combinatorial sieve for estimating the number of points on V for which a fixed set of integral polynomials take prime or almost prime values. A crucial role is played by the expansion property of the congruence graphs' that we associate with V . This expansion property is established when  . To cite this article: J. Bourgain et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
Résumé

Soit V lʼorbite dans   dʼun sous-groupe finiment engendré de   donʼt lʼadhérence dans la topologie de Zariski est suffisament grande (p.e. est isomorphe à  ). Nous developpons une crible combinatoire de Brun a fin dʼestimer le nombre de points de V pour lesquels un system de polynômes donnés prennent des valeurs premières ou presque premières. Des propriétés dʼexpansion de certain « graphes de congruence » y jouent un rôle crucial, quʼon établi dans le cas  . Pour citer cet article : J. Bourgain et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).

The full text of this article is available in PDF format.
  The first author was supported in part by NSF grant DMS-0322370. The second author was supported in part by NSF grant DMS-0111298 and DMS-0501245. The third author was supported in part by Oscar Veblen Fund (IAS) and the NSF.


© 2006  Académie des sciences@@#104156@@
EM-CONSULTE.COM is registrered at the CNIL, déclaration n° 1286925.
As per the Law relating to information storage and personal integrity, you have the right to oppose (art 26 of that law), access (art 34 of that law) and rectify (art 36 of that law) your personal data. You may thus request that your data, should it be inaccurate, incomplete, unclear, outdated, not be used or stored, be corrected, clarified, updated or deleted.
Personal information regarding our website's visitors, including their identity, is confidential.
The owners of this website hereby guarantee to respect the legal confidentiality conditions, applicable in France, and not to disclose this data to third parties.
Close
Article Outline
You can move this window by clicking on the headline
@@#110903@@