Ergodic theoretic proof of equidistribution of Hecke points

By A. Eskin, H. Oh. Ergodic Theory and Dynamical Systems, 2004

48 citations recorded by the source corpus.

We prove the equidistribution of Hecke points for any connected non-compact $\mathbb{Q}$-simple real algebraic group G and an arithmetic subgroup $\Gamma\subset G(\mathbb{Q})$, generalizing a theorem of Clozel, Oh and Ullmo. The main tool is a theorem of Mozes and Shah on unipotent flows.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c3a52f91c2e7b68a7be0e816476a547d3e118128

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Manin's and Peyre's conjectures on rational points and adelic mixing (2006, background): “rator Ta on L2(Γ\G S) is deﬁned by Ta(f)(g) = 1 deg(a) X x∈Γ\ΓaΓ f(xg) where deg(a) = #Γ\ΓaΓ. Theorem 1.17 extends the main result in [COU] where some cases of Q-anisotropic groups were excluded (see [EO]). In fact, the following corollary immediately follows from Theorem 1.17 and Proposition 2.6 in”
Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces (2007, methodology): “” See [21] for details of translating equidistribution of H-orbits to statements in the style of Proposition 17.”
Stationary measures and invariant subsets of homogeneous spaces (III) (2013, result): “It also extends previous results by Clozel, Oh and Ullmo in [9] about equidistribution of Hecke orbits (see also [13]).”
Stationary measures and invariant subsets of homogeneous spaces (II) (2013, result): “It also extends previous results by Clozel, Oh and Ullmo in [9] about equidistribution of Hecke orbits (see also [13]).”