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Langlands Conjectures for GLn

  • J. W. Cogdell

Abstract

One of the principle goals of modern number theory is to understand the Galois group G k = Gal(̄k/k) of a local or global field k, such as ℚ for example. One way to try to understand the group G k is by understanding its finite dimensional representation theory. In the case of a number field, to every finite dimensional representation ρ : G k → GL n (ℂ) Artin attached a complex analytic invariant, its L-function L(s, ρ). One approach to understanding ρ is through this invariant. For one dimensional ρ this idea was fundamental for the analytic approach to abelian class field theory and the understanding of G k ab . To obtain a more complete understanding of G k we would hope for a more complete understanding of the L(s, ρ) for higher dimensional representations.

Keywords

Modular Form Galois Group Automorphic Form Galois Representation Automorphic Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • J. W. Cogdell

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