Manin's and Peyre's conjectures on rational points and adelic mixing
Number Theory
2008-02-13 v5 Representation Theory
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.
Keywords
Cite
@article{arxiv.math/0601127,
title = {Manin's and Peyre's conjectures on rational points and adelic mixing},
author = {Alex Gorodnik and Francois Maucourant and Hee Oh},
journal= {arXiv preprint arXiv:math/0601127},
year = {2008}
}
Comments
to appear in Ann. Sci. Ecole Norm. Sup