## Abstract

A family of global zeta integrals representing a product of tensor product (partial) L-functions: (Formula presented.)is established in this paper, where π is an irreducible cuspidal automorphic representation of a quasi-split classical group of Hermitian type and τ_{1},...,τ_{r} are irreducible unitary cuspidal automorphic representations of GL_{a1},...,GL_{ar}, respectively. When r = 1 and the classical group is an orthogonal group, this family was studied by Ginzburg et al. (Mem Am Math Soc 128: viii+218, 1997). When π is generic and τ_{1},...,τ_{r} are not isomorphic to each other, such a product of tensor product (partial) L-functions is considered by Ginzburg et al. (The descent map from automorphic representations of GL(n) to classical groups, World Scientific, Singapore, 2011) in with different kind of global zeta integrals. In this paper, we prove that the global integrals are eulerian and finish the explicit calculation of unramified local zeta integrals in a certain case (see Section 4 for detail), which is enough to represent the product of unramified tensor product local L-functions. The remaining local and global theory for this family of global integrals will be considered in our future work.

Original language | English (US) |
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Pages (from-to) | 552-609 |

Number of pages | 58 |

Journal | Geometric and Functional Analysis |

Volume | 24 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2014 |

### Bibliographical note

Funding Information:Keywords and phrases: Bessel periods of Eisenstein series, global zeta integrals, tensor product L-functions, classical groups of Hermitian type Mathematics Subject Classification: Primary 11F70, 22E50; Secondary 11F85, 22E55 The work of D. Jiang is supported in part by the NSF Grants DMS-1001672 and DMS-1301567.

## Keywords

- 22E50
- 22E55
- Bessel periods of Eisenstein series
- Primary 11F70
- Secondary 11F85
- classical groups of Hermitian type
- global zeta integrals
- tensor product L-functions