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Rational points on compactifications of semi-simple groups

Authors: Joseph Shalika, Ramin Takloo-Bighash and Yuri Tschinkel
Journal: J. Amer. Math. Soc. 20 (2007), 1135-1186
MSC (2000): Primary 14G05, 11G50; Secondary 11F70
Published electronically: May 11, 2007
MathSciNet review: 2328719
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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.

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Additional Information

Joseph Shalika
Affiliation: Department of Mathematics, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218-2686

Ramin Takloo-Bighash
Affiliation: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000

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

Keywords: Manin's conjectures, rational points, wonderful compactifications, automorphic forms
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
Article copyright: © Copyright 2007 American Mathematical Society