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Let k be a local field of characteristic not 2, and let G be the group of k-rational points of a connected reductive linear algebraic group defined over k with a simple derived group of k-rank at least 2. We construct new uniform pointwise bounds for the matrix coefficients of all infinite-dimensional irreducible unitary representations of G. These bounds(More)
Let f be a homogeneous polynomial in n variables with integer coefficients. For any integer m, consider the affine subvariety of R n defined by V m = {x ∈ R n : f (x) = m}. It is a classical problem in number theory to understand the distribution of the set V m (Z) of integer points in V m. Two basic types of questions have been studied in the literature.(More)
For G = SL(3, R) and G = SO(2, n), we give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G has the property that there exists a compact subset C of G with CHC = G. To do this, we fix a Cartan decomposition G = KA + K of G, and then carry out an approximate calculation of (KHK) ∩ A + for each closed, connected(More)