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manuscripta mathematica

, Volume 110, Issue 3, pp 283–311 | Cite as

Critical values of automorphic L-functions for GL(r)×GL(r)

  • Loïc Grenié
  • 74 Downloads

Abstract.

 We compute, up to an element of a fixed number field, the critical values of the L-function of a pair of automorphic, cuspidal, cohomological representations of any GL(r). The result is expressed as a product of cohomological periods divided by an archimedean integral. The main tool used is the rationality of the cohomology of the three representations involved in the Rankin–Selberg integral. As an intermediate step, we also obtained the rationality of the Eisenstein cohomology.

Keywords

Fixed Number Main Tool Intermediate Step Number Field Cohomological 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Loïc Grenié
    • 1
  1. 1.Université Paris 7. and Max-Planck-Institut für Mathematik. e-mail: grenie@math.jussieu.frFR

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