Manin’s and Peyre’s conjectures on rational points and adelic mixing
Alex Gorodnik, François Maucourant, Hee Oh (2008)
Annales scientifiques de l'École Normale Supérieure
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Let be the wonderful compactification of a connected adjoint semisimple group defined over a number field . We prove Manin’s conjecture on the asymptotic (as ) of the number of -rational points of of height less than , and give an explicit construction of a measure on , generalizing Peyre’s measure, which describes the asymptotic distribution of the rational points on . Our approach is based on the mixing property of which we obtain with a rate of convergence. ...