The Degenerate Residual Spectrum of Quasi-Split Forms of Spin₈\n Associated to the Heisenberg Parabolic Subgroup

2018/04/24 by Avner Segal, Segal, Avner
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1804.08849

openalex publication_date 2018/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In citeMR3284482 and citeMR3658191, the twisted standard\n\L-function \L(s,\π,\χ,st) of a cuspidal\nrepresentation \π of the exceptional group of type G₂ was shown to be\nrepresented by a family of new-way Rankin-Selberg integrals. These integrals\nconnect the analytic behaviour of \L(s,\π,\χ,st) with that of a\nfamily of degenerate Eisenstein series \E_E(\χ, f_s, s, g) on\nquasi-split forms H_E of Spin₈, induced from Heisenberg parabolic\nsubgroups. The analytic behaviour of the series \E_E(\χ, f_s, s,\ng) in the right half-plane Re(s)>0 was studied in citeSegalEisen. In this\npaper we study the residual representations associated with\n\E_E(\χ, f_s, s, g).\n

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