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- Q6486191 subject Q7029575.
- Q6486191 subject Q8653246.
- Q6486191 subject Q9943692.
- Q6486191 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.".
- Q6486191 wikiPageExternalLink books?id=_QDvAAAAMAAJ.
- Q6486191 wikiPageExternalLink pspum332.
- Q6486191 wikiPageWikiLink Q17104667.
- Q6486191 wikiPageWikiLink Q176916.
- Q6486191 wikiPageWikiLink Q1868517.
- Q6486191 wikiPageWikiLink Q2076913.
- Q6486191 wikiPageWikiLink Q2584927.
- Q6486191 wikiPageWikiLink Q2993300.
- Q6486191 wikiPageWikiLink Q32229.
- Q6486191 wikiPageWikiLink Q4958218.
- Q6486191 wikiPageWikiLink Q7029575.
- Q6486191 wikiPageWikiLink Q7687933.
- Q6486191 wikiPageWikiLink Q8653246.
- Q6486191 wikiPageWikiLink Q9943692.
- Q6486191 comment "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.".
- Q6486191 label "Langlands–Deligne local constant".