Effective equidistribution of S-integral points on symmetric varieties

By Y. Benoist, H. Oh. 2007

93 citations recorded by the source corpus.

Let K be a global field of characteristic not 2. Let Z be a symmetric variety defined over K and S a finite set of places of K. We obtain counting and equidistribution results for the S-integral points of Z. Our results are effective when K is a number field.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9f37352bd7c9bcaeedcfb64f7d507ffd04946727

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Matrix coefficients, counting and primes for orbits of geometrically finite groups (2012, methodology): “For > 0, we choose τ ∈ C(Y) which is an H ∩M-invariant smooth approximation of the set Y : 0 ≤ τ ≤ 1, τ (x) = 1 for x ∈ Y and τ (x) = 0 for x / ∈ Y /2; we refer to [4] for the construction of such τ .”
Rational Points on Homogeneous Varieties and Equidistribution of Adelic Periods (2008, methodology): “Establishing this is based on the work of Chambert-Loir and Tschinkel [20] and of Benoist-Oh [10] (also [37] of Gorodnik-Nevo).”
Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces (2007, methodology): “We will be using this construction for various choices of the function f and the domain V to obtain various subspaces of W = g, and the following remark will help to compare their dimension.”
Anosov groups: local mixing, counting and equidistribution (2020, background): “Counting in affine symmetric spaces Around 1993, Duke, Rudnick and Sarnak [10] and Eskin and McMullen [11] showed the following; see also Benoist and Oh [2], Gorodnik and Oh [13] and Gorodnik, Oh and Shah [14; 15].”