Not signed in (Sign In)

Start a new discussion

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Discussion Tag Cloud

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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.

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)