Langlands Conjectures for GL n

J. W. Cogdell

Chapter 10 in An Introduction to the Langlands Program, 2004, pp 229-249 from Springer

Abstract: 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 (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-0-8176-8226-2_10

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