## Abstract

Let τ_{1}^{(r)}, τ_{2}^{(r)} be two genuine cuspidal automorphic representations on r-fold covers of the adelic points of the general linear groups GL_{n1}, GL_{n2}, respectively, and let E(g, s) be the associated Eisenstein series on an r-fold cover of GL_{n1+n2}, normalized to have functional equation under s ⟼ 1 - s. Suppose R(s) ≥ 1/2 without loss. Then the value at any point of holomorphy s = s_{0} or the reside at any (simple) pole of E(g, s) is an automorphic form, and generates an automorphic representation. In this note we show that if n_{1} ≠ n_{2} these automorphic representations (when not identically zero) are generic, while if n_{1} = n_{2} := n they are generic except for residues at s = n+1/2n.

Original language | English |
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Pages (from-to) | 1000-1012 |

Number of pages | 13 |

Journal | International Mathematics Research Notices |

Volume | 2017 |

Issue number | 4 |

DOIs | |

State | Published - 2017 |

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