A Product of Tensor Product L-functions of Quasi-split Classical Groups of Hermitian Type

2012/12/29 by Dihua Jiang, Lei Zhang, Jiang, Dihua +1
Mathematics · #11F70 #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1212.6580

openalex publication_date 2012/12/29 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

A family of global integrals representing a product of tensor product (partial) L-functions: L^S(s,π×τ₁)L^S(s,π×τ₂)... L^S(s,π×τ_r) are established in this paper, where π is an irreducible cuspidal automorphic representation of a quasi-split classical group of Hermitian type and τ₁,...,τ_r are irreducible unitary cuspidal automorphic representations of \GL_a1,...,\GL_ar, respectively. When r=1 and the classical group is an orthogonal group, this was studied by Ginzburg, Piatetski-Shapiro and Rallis in 1997 and when π is generic and τ₁,...,τ_r are not isomorphic to each other, this is considered by Ginzburg, Rallis and Soudry in 2011. In this paper, we prove that the global integrals are eulerian and finish the explicit calculation of unramified local L-factors in general. The remaining local and global theory for this family of global integrals will be considered in our future work.

Citations

• Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups
• Rankin-Selberg Convolutions

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