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arXiv · math/0601127

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

Alex Gorodnik·Francois Maucourant·Hee Oh
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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\to \infty) 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 L^2(G(K)\G(A)) which we obtain with a rate of convergence.

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Alex Gorodnik, Francois Maucourant, Hee Oh. 2008-02-12. Manin's and Peyre's conjectures on rational points and adelic mixing. https://arxiv.org/abs/math/0601127

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