Rational points on compactifications of semi-simple groups

Shalika, Joseph; Takloo-Bighash, Ramin; Tschinkel, Yuri

doi:10.1090/S0894-0347-07-00572-3

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

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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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