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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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The affine sieve
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by Alireza Salehi Golsefidy and Peter Sarnak PDF
J. Amer. Math. Soc. 26 (2013), 1085-1105 Request permission

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
  • MR Author ID: 154725
  • Email: sarnak@math.princeton.edu
  • 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
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 26 (2013), 1085-1105
  • MSC (2010): Primary 20G35, 11N35
  • DOI: https://doi.org/10.1090/S0894-0347-2013-00764-X
  • MathSciNet review: 3073885