## Abstract

Let F be a p-adic field, let χ be a character of F^{*}, let ψ be a character of F and let γ_{ψ} be the normalized Weil factor associated with a character of second degree. We prove here that one can define a meromorphic function (χ, s, ψ) via a similar functional equation to the one used for the definition of the Tate γ-factor replacing the role of the Fourier transform with an integration against ψ. γ_{ψ}^{-1}. It turns out that γ and have similar integral representations. Furthermore, has a relation to Shahidi's metaplectic local coefficient which is similar to the relation γ has with (the non-metalpectic) Shahidi's local coefficient. Up to an exponential factor, (χ, s, ψ) is equal to the ratio.

Original language | English |
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Pages (from-to) | 45-53 |

Number of pages | 9 |

Journal | Ramanujan Journal |

Volume | 26 |

Issue number | 1 |

DOIs | |

State | Published - Oct 2011 |

Externally published | Yes |

## Keywords

- Local coefficients
- Tate gamma-factor
- The metaplectic group
- Weil factor of character of second degree