The conjecture that the Artin L-function of any 
-dimensional
complex representation of the Galois group of a finite
extension of the rational numbers 
is an Artin L-function
obtained from the general linear group 
.
Langlands Reciprocity
See also
Artin L-Function, Langlands ProgramExplore with Wolfram|Alpha
References
Knapp, A. W. "Group Representations and Harmonic Analysis, Part II." Not. Amer. Math. Soc. 43, 537-549, 1996.Referenced on Wolfram|Alpha
Langlands ReciprocityCite this as:
Weisstein, Eric W. "Langlands Reciprocity." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LanglandsReciprocity.html