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Langlands-Deligne local constant
Definición
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In mathematics, the Langlands–Deligne local constant, also known as the local epsilon factor or local Artin root number (up to an elementary real function of s), is an elementary function associated with a representation of the Weil group of a local field. The functional equation
- L(ρ,s) = ε(ρ,s)L(ρ∨,1−s)
of an Artin L-function has an elementary function ε(ρ,s) appearing in it, equal to a constant called the Artin root number times an elementary real function of s, and Langlands discovered that ε(ρ,s) can be written in a canonical way as a product
- ε(ρ,s) = Π ε(ρv, s, ψv)
of local constants ε(ρv, s, ψv) associated to primes v.
Tate proved the existence of the local constants in the case that ρ is 1-dimensional in Tate's thesis.
Dwork (1956) proved the existence of the local constant ε(ρv, s, ψv) up to sign.
The original proof of the existence of the local constants by Langlands (1970) used local methods and was rather long and complicated, and never published. Deligne (1973) later discovered a simpler proof using global methods.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Langlands%E2%80%93Deligne_local_constant)
Concepto genérico
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URI
http://data.loterre.fr/ark:/67375/PSR-MN23KDNV-D
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