## Abstract

Let E(⋯) be an Eisenstein series corresponding to an automorphic cuspidal representation τ of GLn(A)$, induced to a representation of SO2n+1(A)$ through the Siegel parabolic subgroup. The presence of a pole of E at 12, or the nonvanishing of the residue E_{1/2}, is determined by the presence of a pole of the partial symmetric square L-function at s=1. We define a co-period integral of E, involving the integration of E_{1/2} against a pair of automorphic forms in the space of the small representation of Bump, Friedberg, and Ginzburg. We compute the co-period and relate it to a "theta period" integral of τ - an integral of a cusp form against two theta functions corresponding to the exceptional representation of Kazhdan and Patterson.

Original language | English |
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Pages (from-to) | 2168-2209 |

Number of pages | 42 |

Journal | International Mathematics Research Notices |

Volume | 2015 |

Issue number | 8 |

DOIs | |

State | Published - 2015 |

Externally published | Yes |

### Bibliographical note

Publisher Copyright:© 2014 © The Author(s) 2014.

### Funding

This work was supported in part by the Israel Science Foundation—Centers of Excellence (grant

Funders | Funder number |
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Israel Science Foundation | |

Israeli Centers for Research Excellence |