### Abstract

In this paper, the proof of the finite-field-analogue of Jacquet's conjecture on local converse theorem for cuspidal representations of general linear groups is given. More precisely, the set of twisted gamma factors of π, together with a central character ω_{π}, determine uniquely (up to isomorphism) the irreducible cuspidal representation π of GL_{n} (F_{q}), where G_{t} denotes the set of irreducible generic representations of GL_{t}(F_{q}), and F_{q} denotes a finite field of q elements.

Original language | English |
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Pages (from-to) | 653-674 |

Number of pages | 22 |

Journal | American Journal of Mathematics |

Volume | 136 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2014 Jan 1 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

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## Cite this

Nien, C. (2014). A proof of the finite field analogue of Jacquet's conjecture.

*American Journal of Mathematics*,*136*(3), 653-674. https://doi.org/10.1353/ajm.2014.0020