Automorphic Plancherel density theorem

@article{Shin2012AutomorphicPD,
  title={Automorphic Plancherel density theorem},
  author={S. Shin},
  journal={Israel Journal of Mathematics},
  year={2012},
  volume={192},
  pages={83-120}
}
  • S. Shin
  • Published 2012
  • Mathematics
  • Israel Journal of Mathematics
Let F be a totally real field, G a connected reductive group over F, and S a finite set of finite places of F. Assume that G(F ⊗ℚ ℝ) has a discrete series representation. Building upon work of Sauvageot, Serre, Conrey-Duke-Farmer and others, we prove that the S-components of cuspidal automorphic representations of $$G\left( {\mathbb{A}_F } \right)$$ are equidistributed with respect to the Plancherel measure on the unitary dual of G(FS) in an appropriate sense. A few applications are given, such… Expand
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