Recorded the basic idea at Artin L-function
Also: added the following paragraph to the Idea-section at Langlands correspondence (below the numbered two items stating the conjectured correspondence between Galois representations and automorphic representations):
]]>Moreover, to each such automorphic representation is associated an L-function – the automorphic L-function – and in generalization of Artin reciprocity the conjecture is that the Artin L-function associated with the given Galois representation is equal to the automorphic L-function of the corresponding automorphic representation.