Determination of \textrmGL(3) cusp forms by central values of quadratic twisted L-functions

2022/01/03 by Shenghao Hua, Bingrong Huang, Hua, Shenghao +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.00473

openalex publication_date 2022/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let ϕ and ϕ' be two \textrmGL(3) Hecke--Maass cusp forms. In this paper, we prove that ϕ=ϕ'\textrm or \widetildeϕ' if there exists a nonzero constant κ such that L((1)/(2),ϕ⊗ χ_8d)=κL((1)/(2),ϕ'⊗ χ_8d) for all positive odd square-free positive d. Here \widetildeϕ' is dual form of ϕ' and χ_8d is the quadratic character ((8d)/(⋅)). To prove this, we obtain asymptotic formulas for twisted first moment of central values of quadratic twisted L-functions on \textrmGL(3), which will have many other applications.

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