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)
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