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Mathematics > Representation Theory

arXiv:1804.08849 (math)
[Submitted on 24 Apr 2018]

Title:The Degenerate Residual Spectrum of Quasi-Split Forms of $Spin_8$ Associated to the Heisenberg Parabolic Subgroup

Authors:Avner Segal
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Abstract:In \cite{MR3284482} and \cite{MR3658191}, the twisted standard $\mathcal{L}$-function $\mathcal{L}(s,\pi,\chi,st)$ of a cuspidal representation $ \pi$ of the exceptional group of type $G_2$ was shown to be represented by a family of new-way Rankin-Selberg integrals. These integrals connect the analytic behaviour of $\mathcal{L}(s,\pi,\chi,st)$ with that of a family of degenerate Eisenstein series $\mathcal{E}_E(\chi, f_s, s, g)$ on quasi-split forms $H_E$ of $Spin_8$, induced from Heisenberg parabolic subgroups. The analytic behaviour of the series $\mathcal{E}_E(\chi, f_s, s, g)$ in the right half-plane $Re(s)>0$ was studied in \cite{SegalEisen}. In this paper we study the residual representations associated with $\mathcal{E}_E(\chi, f_s, s, g)$.
Subjects: Representation Theory (math.RT); Number Theory (math.NT)
Cite as: arXiv:1804.08849 [math.RT]
  (or arXiv:1804.08849v1 [math.RT] for this version)
  https://doi.org/10.48550/arXiv.1804.08849

Submission history

From: Avner Segal [view email]
[v1] Tue, 24 Apr 2018 06:07:04 UTC (61 KB)
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