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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

The affine sieve


Authors: Alireza Salehi Golsefidy and Peter Sarnak
Journal: J. Amer. Math. Soc. 26 (2013), 1085-1105
MSC (2010): Primary 20G35, 11N35
Published electronically: April 1, 2013
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Abstract: We establish the main saturation conjecture connected with executing a Brun sieve in the setting of an orbit of a group of affine linear transformations. This is carried out under the condition that the Zariski closure of the group is Levi-semisimple. It is likely that this condition is also necessary for such saturation to hold.


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Additional Information

Alireza Salehi Golsefidy
Affiliation: Department of Mathematics, University of California, San Diego, California 92093-0112
Email: golsefidy@ucsd.edu

Peter Sarnak
Affiliation: Department of Mathematics, Princeton University, Princeton, New Jersey 08544-1000
Email: sarnak@math.princeton.edu

DOI: http://dx.doi.org/10.1090/S0894-0347-2013-00764-X
PII: S 0894-0347(2013)00764-X
Received by editor(s): October 13, 2011
Received by editor(s) in revised form: January 7, 2013
Published electronically: April 1, 2013
Additional Notes: The first author was partially supported by the NSF grants DMS-0635607 and DMS-1001598
The second author was partially supported by an NSF grant
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.