Tate γ -factor, Weil index, and the metaplectic γ~ -factor

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Let F be a p-adic field, let ψ be a non-trivial character of F, and let χ be a character of F. In this short note we present two new identities involving γ(s, χ, ψ) , γ(ψ) , and γ~ (s, χ, ψ) along with a duplication formula for γ(s, χ, ψ). Here γ(s, χ, ψ) is the Tate γ-factor, γ(ψ) is the Weil index, and γ~ (s, χ, ψ) is the metaplectic γ~ -factor. As a result we give a new proof for a useful identity involving these three factors originally proven by W. Jay Sweet.

Original languageEnglish
Pages (from-to)697-706
Number of pages10
JournalRamanujan Journal
Issue number2
StatePublished - 26 Feb 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC part of Springer Nature.


  • Local factors
  • Metaplectic gamma factor
  • Tate gamma factor
  • Weil index


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