A short proof for the relation between Weil indices and factors

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Let F be a finite extension of ℚp and let ψ be a non-trivial character of F. For a∈F* let γ(a,ψ) be the normalized Weil index splitting the Hilbert symbol. In this short note we give a simple proof for the relation (Formula presented.) where ηa is the quadratic character of F* whose kernel is N(F√a) and where &(⋅,⋅,⋅) is the epsilon factor appearing in Tate’s thesis.

Original languageEnglish
Pages (from-to)2846-2851
Number of pages6
JournalCommunications in Algebra
Issue number7
StatePublished - 3 Jul 2018
Externally publishedYes

Bibliographical note

Funding Information:
The author is partially supported by a Simons Foundation Collaboration Grant 426446.

Publisher Copyright:
© 2017 Taylor & Francis.


  • Epsilon factor
  • Hilbert symbol
  • Weil index
  • local factors


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