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Langlands Conjectures for GL n

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Book cover An Introduction to the Langlands Program

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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 ab k . 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.

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Authors
  1. J. W. Cogdell
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Editors and Affiliations

  1. Department of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv, 69978, Israel

    Joseph Bernstein

  2. Department of Mathematics, The Weizmann Institute of Science, Rehovot, 76100, Israel

    Stephen Gelbart

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Cogdell, J.W. (2004). Langlands Conjectures for GL n . In: Bernstein, J., Gelbart, S. (eds) An Introduction to the Langlands Program. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8226-2_10

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  • DOI: https://doi.org/10.1007/978-0-8176-8226-2_10

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-0-8176-3211-3

  • Online ISBN: 978-0-8176-8226-2

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