Rationality for isobaric automorphic representations: the CM-case

摘要

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,Π×Π′) (Grobner and Harris in J Inst Math Jussieu 15:711–769, , Thm. 3.9) to (i) general CM-fields F and (ii) cohomological automorphic representations Π′=Π1⊞⋯⊞Πk which are the isobaric sum of unitary cuspidal automorphic representations Πi of general linear groups of arbitrary rank over F. In this sense, the main result of these notes, cf. Theorem , is a generalization, as well as a complement, of the main results in Raghuram (Forum Math 28:457–489, ; Int Math Res Not 2:334–372, . ), and Mahnkopf (J Inst Math Jussieu 4:553–637, ).