Lifting, restricting and sifting integral points on affine homogeneous varieties
نویسندگان
چکیده
منابع مشابه
Density of Integer Points on Affine Homogeneous Varieties
A basic problem of diophantine analysis is to investigate the asymptotics as T of (1.2) N(T, V)= {m V(Z): Ilmll T} where we denote by V(A), for any ring A, the set of A-points of V. Hence I1" is some Euclidean norm on R". The only general method available for such problems is the Hardy-Littlewood circle method, which however has certain limitations, requiring roughly that the codimension of V i...
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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 e...
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Let V be an affine symmetric variety defined over Q. We compute the asymptotic distribution of the angular components of the integral points in V . This distribution is described by a family of invariant measures concentrated on the Satake boundary of V . In the course of the proof, we describe the structure of the Satake compactifications for general affine symmetic varieties and compute the a...
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ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2012
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x12000516