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.
Bibliographical noteFunding Information:
The author is partially supported by a Simons Foundation Collaboration Grant 426446.
© 2017 Taylor & Francis.
- Epsilon factor
- Hilbert symbol
- Weil index
- local factors