Rationality for isobaric automorphic representations: the CM-case

@article{Grobner2018RationalityFI,
  title={Rationality for isobaric automorphic representations: the CM-case},
  author={Harald Grobner},
  journal={Monatshefte Fur Mathematik},
  year={2018},
  volume={187},
  pages={79 - 94}
}
  • H. Grobner
  • Published 21 May 2018
  • Mathematics
  • Monatshefte Fur Mathematik
In this note we prove a simultaneous extension of the author’s joint result with M. Harris for critical values of Rankin–Selberg L-functions $$L(s,\Pi \times \Pi ')$$L(s,Π×Π′) (Grobner and Harris in J Inst Math Jussieu 15:711–769, 2016, Thm. 3.9) to (i) general CM-fields F and (ii) cohomological automorphic representations $$\Pi '=\Pi _1\boxplus \cdots \boxplus \Pi _k$$Π′=Π1⊞⋯⊞Πk which are the isobaric sum of unitary cuspidal automorphic representations $$\Pi _i$$Πi of general linear groups of… 
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