## Abstract

Let π be an irreducible admissible representation of GL_{m}(F) , where F is a non-archimedean local field of characteristic zero. In 1990’s Jacquet and Shalika established an integral representation for the exterior square L-function. We complete, following the method developed by Cogdell and Piatetski-Shapiro, the computation of the local exterior square L-function L(s, π, ∧ ^{2}) via the integral representation in terms of L-functions of supercuspidal representations by a purely local argument. With this result, we show the equality of the local analytic L-functions L(s, π, ∧ ^{2}) via the integral representation for the irreducible admissible representation π for GL_{m}(F) and the local arithmetic L-functions L(s, ∧ ^{2}(ϕ(π))) of its Langlands parameter ϕ(π) through local Langlands correspondence.

Original language | English |
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Pages (from-to) | 1687-1725 |

Number of pages | 39 |

Journal | Mathematische Zeitschrift |

Volume | 294 |

Issue number | 3-4 |

DOIs | |

State | Published - 1 Apr 2020 |

### Bibliographical note

Publisher Copyright:© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.

## Keywords

- Bernstein–Zelevinsky derivatives
- Exceptional poles
- Jacquet–Shalika integral
- Local exterior square L-function

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