Manin's and Peyre's conjectures on rational points and adelic mixing

Alexander Gorodnik, F Maucourant, H Oh

Research output: Contribution to journalArticle (Academic Journal)peer-review

Abstract

Let X be the wonderful compactification of a connected adjoint semisimple
group G defined over a number field. We prove Manin’s conjecture on the asymptotic
(as T ! 1) of the number of K-rational points of X of height less than
T, and give an explicit construction of a measure on X(A), generalizing Peyre’s
measure, which describes the asymptotic distribution of the rational points G(K)
on X(A). Our approach is based on the mixing property of L2(G(K)\G(A)) which
we obtain with a rate of convergence.
Translated title of the contributionManin's and Peyre's conjectures on rational points and adelic mixing
Original languageEnglish
Pages (from-to)385-437
Number of pages51
JournalAnnales Scientifiques de l'École Normale Supérieure
Volume41
Issue number3
Publication statusPublished - May 2008

Fingerprint

Dive into the research topics of 'Manin's and Peyre's conjectures on rational points and adelic mixing'. Together they form a unique fingerprint.

Cite this