This paper studies Emerton’s Jacquet module functor for locally analytic representations of p-adic reductive groups, introduced in [Eme06a]. When P is a parabolic subgroup whose Levi factor M is not commutative, we show that passing to an isotypical subspace for the derived subgroup ofM gives rise to essentially admissible locally analytic representations of the torus Z(M), which have a natural...

For automorphic representations in the nontempered cuspidal spectrum of SO5, we establish a precise Bessel period formula, in which the square of the global Bessel period is decomposed as an Euler product of regularized local Bessel period integrals of matrix coefficients.

For any unitary cuspidal representations πn of GLn(QA), n = 2, 3, 4, respectively, consider two automorphic representations Π and Π of GL6(QA), where Πp ∼= ∧π4,p for p 6= 2, 3 and π4,p not supercuspidal, and Π = π2 π3. First, Hypothesis H for Π and Π is proved. Then contributions from prime powers are removed from the prime number theorem for cuspidal representations π and π of GLm(QA) and GLm′...

In this paper, we study the asymptotic behavior of traces Hecke operators for spherical discrete automorphic representations fixed level on general split reductive groups over \(\mathbb {Q}\). Under a condition analytic intertwining operators, which is known classical and exceptional group \(G_2\), obtain expected asymptotics in terms Plancherel measure an explicit estimate remainder.

Let G be a split adjoint group defined over Fq , let F = Fq(t), and let A be the adèles of F. We describe the local constituents at two points of automorphic representations of G in the discrete part of L2(G(F)\G(A)) which have vectors invariant under Iwahori subgroups at these two points and are unramified at all other points.