Manin's and Peyre's conjectures on rational points and adelic mixing
Alex Gorodnik, Francois Maucourant, Hee Oh
Abstract
Let X be the wonderful compactification of a connected adjoint semisimple group G defined over a number field K. We prove Manin's conjecture on the asymptotic (as T ∞) 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)(A)) which we obtain with a rate of convergence.
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