Matches in DBpedia 2015-10 for { ?s ?p "In mathematics, the Langlands–Deligne local constant (or local Artin root number up to an elementary 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 productε(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."@en }
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- Langlands–Deligne_local_constant abstract "In mathematics, the Langlands–Deligne local constant (or local Artin root number up to an elementary 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 productε(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.".