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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeAug 28th 2014

    gave automorphic L-function a minimum of an Idea-section, presently it reads as follows:


    An automorphic L-function L πL_\pi is an L-function built from an automorphic representation π\pi, in nonabelian generalization of how a Dirichlet L-function L χL_\chi is associated to a Dirichlet character χ\chi (which is an automorphic form on the (abelian) idele group).

    In analogy to how Artin reciprocity implies that to every 1-dimensional Galois representation σ\sigma there is a Dirichlet character χ\chi such that the Artin L-function L σL_\sigma equals the Dirichlet L-function L χL_\chi, so the conjectured Langlands correspondence says that to every nn-dimensional Galois representation σ\sigma there is an automorphic representation π\pi such that the automorphic L-function L πL_\pi equals the Artin L-function L σL_\sigma.


    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 17th 2015
    • (edited Jul 17th 2015)

    added at the beginning of the Idea section briefly the conceptual statement that passing from an automorphic form to its automorphic L-function is the generalization of the Mellin transform taking an automorphic form to its zeta function.

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