Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants

By H. Oh. 2002

185 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df1ea1505cc8f219dff20c6e5fe83dc5502d0905

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Citations in the corpus

Manin's and Peyre's conjectures on rational points and adelic mixing (2006, methodology): “[40]): for each g = kadk′ ∈ UvAv ΩvUv, ξv(g) = ∏”
Effective equidistribution of S-integral points on symmetric varieties (2007, background): “20 of [25] based on the results of [8] and [43].”
Rational Points on Homogeneous Varieties and Equidistribution of Adelic Periods (2008, background): “The proof in [36] is based on the information on local harmonic analysis of the groups G(Kv) [54] as well as the automorphic theory of G [18], and gives a rate of convergence.”
Counting lattice points (2009, background): “Verification of these claims depends on the fact that matrix coe‰cients of nontrivial irreducible representations p of almost simple simply connected groups are in L p for some p 1⁄4 pðpÞ (see [11], [19], [46], [47], [57], [58], [73]).”
Anosov groups: local mixing, counting and equidistribution (2020, background): “On the other hand, when Γ is of infinite co-volume in a simple Lie group of rank at least 2, Quint deduced from [24] that ψΓ ≤ 2(ρ−ηG), where 2ηG is the sum of the maximal strongly orthogonal subset of the root system of G [36].”
Sparse equidistribution problems, period bounds and subconvexity (2005, background): “1) is proven in [10] (strictly this is for semisimple groups, and the generalization to reductive groups is established in [30]).”
The subconvexity problem for GL2 (2009, background): “It follows from [13] (as extended to reductive groups in [56]) that, if πv is a tempered representation of G(Fv) one has, for any x1, x2 ∈ πv, g ∈ Gv and some constant d > 0 depending on G only |〈gx1, x2〉| 6 AvS d (x1)S πv d (x2)Ξv(g), where Av = [Kv : Kv[0]] is equal to 1 for almost all v.”
On the growth of Betti numbers of locally symmetric spaces (2011, background): “3 and a quantitative version of the Howe–Moore theorem due to Howe and Oh [12], one can prove the following key result:”
Rational Points on Compactifications of Semi-Simple Groups of Rank 1 (2006, unknown): “2 ([29], Theorem 1.”
Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces (2007, background): “Oh and Gorodnik-Maucourant-Oh: [47] and [24, Cor 3.26]; these results give explicit (and “good”) rates of decay for matrix coefficients.”
On the growth of $L^2$-invariants for sequences of lattices in Lie groups (2012, background): “[90], we conclude that there exists a positive constant α such that”