L-functions for Sp(2n)\timesGL(k) via non-unique models

2023/03/05 by Yubo Jin, Jin, Yubo, Pan Yan +1
Mathematics · #22E50 #22E55 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #Primary 11F70 #Representation Theory (math.RT) #Secondary 11F55

paper · pdf · doi:10.48550/arxiv.2303.02544

openalex publication_date 2023/03/05 · openalex created_date 2023/03/09 · openalex updated_date 2026/07/28

Abstract

Let n and k be positive integers such that n is even. We derive new global integrals for Sp_2n\timesGL_k from the generalized doubling method of Cai, Friedberg, Ginzburg and Kaplan, following a strategy and extending a previous result of Ginzburg and Soudry on the case n=k=2. We show that these new integrals unfold to non-unique models on Sp_2n. Using the New Way method of Piatetski-Shapiro and Rallis, we show that these new global integrals represent the L-functions for Sp_2n\timesGL_k, generalizing a previous result of the second-named author on Sp₄\timesGL₂ and a previous work of Piatetski-Shapiro and Rallis on Sp_2n\timesGL₁.

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