David Ginzburg

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Let π1 and π2 be irreducible unitary cuspidal automorphic representations of GLm(A) and GLn(A), respectively, where A is the ring of adeles attached to a number field k. The basic analytic properties (meromorphic continuation and the functional equation) of the Rankin-Selberg L-functions L(s, π1 × π2) have been established through the work [JPSS83], [CPS04](More)
In this note, we introduce a global integral of Rankin-Selberg and Shimura type, which represents the tensor L-function of a pair of irreducible, cuspidal, automorphic representations of Sp2k(A) and GLm(A), respectively. This construction is completely general and applies to any cuspidal representation of the symplectic group. We use this construction to(More)
We characterize the nonvanishing of the central value of the Rankin-Selberg L-functions L(s, π × π′) in terms of the period of the GrossPrasad type for the case where π is an irreducible cuspidal automorphic representation of GL2r(A) of symplectic type and π ′ is an irreducible cuspidal automorphic representation of GL2l(A) of orthogonal type. The other(More)
We bound the first occurrence in the theta correspondence of irreducible cuspidal automorphic representations σ of orthogonal groups, in terms of their generalized Gelfand-Graev periods. We also obtain a local analog at a finite place. As a result, we determine a range of holomorphy of LS(s, σ) in the right half plane in terms of the local generalized(More)
0. Introduction. Let τ be an irreducible, automorphic, cuspidal, self-dual representation of GL2n(A), where A is the adele ring of a number field F . Assume that the partial exterior square L-function L(τ, 2, s) has a pole at s = 1 and that the standard L-function L(τ,(1/2)) = 0. In [GRS1] we constructed a space πψ(τ) of cusp forms on the metaplectic cover(More)
The notion of a tower of Rankin-Selberg integrals was introduced in [G-R]. To recall this notion, let G be a reductive group defined over a global field F . Let G denote the L group of G. Let ρ denote a finite dimensional irreducible representation of G. Given an irreducible generic cuspidal representation of G(A), we let L(π, ρ, s) denote the partial L(More)
In 2005, Ginzburg, Rallis and Soudry constructed, in terms of residues of certain Eisenstein series, and by use of the descent method, families of non-tempered automorphic representations of Sp4nm(A) and S̃p2n(2m−1)(A), which generalized the classical work of Piatetski-Shapiro on Saito-Kurokawa liftings. In this paper, we introduce a new framework (Diagrams(More)
Let π denote an irreducible generic cuspidal automorphic representation of SO2m+1(A). Here A is the ring of adeles of a number field F . We say that π is an endoscopic representation with respect to SO2r+1×SO2(m−r)+1 if there are generic cuspidal automorphic representations σ1 and σ2 of SO2r+1(A) and SO2(m−r)+1(A), respectively, such that π is the Langlands(More)