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

In \cite{MR3284482} and \cite{MR3658191}, the twisted standard $L$ -function $L (s, π, χ, s t)$ of a cuspidal representation $π$ 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 $L (s, π, χ, s t)$ with that of a family of degenerate Eisenstein series $E_{E} (χ, f_{s}, s, g)$ on quasi-split forms $H_{E}$ of $S p i n_{8}$ , induced from Heisenberg parabolic subgroups. The analytic behaviour of the series $ $E$ _E(\chi, f_s, s, g) $i n t h e r i g h t h a l f - p l a n e$ Re(s)>0$ was studied in \cite{SegalEisen}. In this paper we study the residual representations associated with $E_{E} (χ, f_{s}, s, g)$ .

The Degenerate Residual Spectrum of Quasi-Split Forms of $S p i n_{8}$ Associated to the Heisenberg Parabolic Subgroup

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The Degenerate Residual Spectrum of Quasi-Split Forms of $S p i n_{8}$ Associated to the Heisenberg Parabolic Subgroup

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The Degenerate Residual Spectrum of Quasi-Split Forms of Spin8Spin8​ Associated to the Heisenberg Parabolic Subgroup

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The Degenerate Residual Spectrum of Quasi-Split Forms of Spin8Spin8​ Associated to the Heisenberg Parabolic Subgroup

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The Degenerate Residual Spectrum of Quasi-Split Forms of $S p i n_{8}$ Associated to the Heisenberg Parabolic Subgroup

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The Degenerate Residual Spectrum of Quasi-Split Forms of $S p i n_{8}$ Associated to the Heisenberg Parabolic Subgroup

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