## Abstract

In [J. Inst. Math. Jussieu 14 (2015), pp. 149-184] and [Int. Math. Res. Not. imrn 7 (2017), pp. 2014-2099], the twisted standard L-function L(s, π, χ, st) 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, st) with that of a family of degenerate Eisenstein series ε_{E}(χ, f_{s}, s, g) on quasi-split forms H_{E} of Spin8, induced from Heisenberg parabolic subgroups. The analytic behaviour of the series ε_{E}(χ, f_{s}, s, g) in the right half-plane Re(s) > 0 was studied in [Tran. Amer. Math. Soc. 370 (2018), pp. 5983-6039]. In this paper we study the residual representations associated with ε_{E}(χ, f_{s}, s, g).

Original language | English |
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Pages (from-to) | 6703-6754 |

Number of pages | 52 |

Journal | Transactions of the American Mathematical Society |

Volume | 372 |

Issue number | 9 |

DOIs | |

State | Published - 1 Nov 2019 |

Externally published | Yes |

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