On the existence of a p-adic metaplectic Tate-type-factor

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Let F be a p-adic field, let χ be a character of F*, let ψ be a character of F and let γψ 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. γψ-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 languageEnglish
Pages (from-to)45-53
Number of pages9
JournalRamanujan Journal
Issue number1
StatePublished - Oct 2011
Externally publishedYes


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


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