# 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} }

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…

## 8 Citations

Relations of rationality for special values of
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In this paper, we prove new cases of Blasius’ and Deligne’s conjectures on the algebraicity of critical values of tensor product L-functions and symmetric odd power L-functions associated to modular…

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We prove the Archimedean period relations for Rankin-Selberg convolutions for GL(n) × GL(n − 1). This implies the period relations for critical values of the Rankin-Selberg L-functions for…

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