Counting orbits of integral points in families of affine homogeneous varieties and diagonal flows
نویسندگان
چکیده
In this paper, we study the distribution of integral points on parametric families of affine homogeneous varieties. By the work of Borel and Harish-Chandra, the set of integral points on each such variety consists of finitely many orbits of arithmetic groups, and we establish an asymptotic formula (on average) for the number of the orbits indexed by their Siegel weights. Our arguments use the exponential mixing property of diagonal flows on homogeneous spaces. 1
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