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

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

2006-01-06

arxiv.org/abs/math/0601127v5

Mathematics

Number Theory

to appear in Ann. Sci. Ecole Norm. Sup

Scientific paper

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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