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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 mathematics.

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

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Rational points on compactifications of semi-simple groups
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by Joseph Shalika, Ramin Takloo-Bighash and Yuri Tschinkel
J. Amer. Math. Soc. 20 (2007), 1135-1186
DOI: https://doi.org/10.1090/S0894-0347-07-00572-3
Published electronically: May 11, 2007

Abstract:

We prove Manin’s conjecture concerning the distribution of rational points of bounded height, and its refinement by Peyre, for wonderful compactifications of semi-simple algebraic groups over number fields. The proof proceeds via the study of the associated height zeta function and its spectral expansion.
References
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Bibliographic Information
  • Joseph Shalika
  • Affiliation: Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218-2686
  • Email: shalika@math.jhu.edu
  • Ramin Takloo-Bighash
  • Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000
  • MR Author ID: 671289
  • Email: rtakloo@math.princeton.edu
  • Yuri Tschinkel
  • Affiliation: Courant Institute, NYU, 251 Mercer Street, New York, New York 10012
  • Address at time of publication: Mathematisches Institut, Bunsenstr. 3-5, 37073 Göttingen, Germany
  • Email: tschinkel@cims.nyu.edu
  • Received by editor(s): February 10, 2006
  • Published electronically: May 11, 2007
  • Additional Notes: The second author was partially supported by the Clay Mathematics Institute and the NSA
    The third author was partially supported by NSF grants 0100277 and 0602333
  • © Copyright 2007 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 20 (2007), 1135-1186
  • MSC (2000): Primary 14G05, 11G50; Secondary 11F70
  • DOI: https://doi.org/10.1090/S0894-0347-07-00572-3
  • MathSciNet review: 2328719