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 arbitrary rank over F. In this sense, the main result of these notes, cf. Theorem 1.9, is a generalization, as well as a complement, of the main results in Raghuram (Forum Math 28:457–489, 2016; Int Math Res Not 2:334–372, 2010. https://doi.org/10.1093/imrn/rnp127), and Mahnkopf (J Inst Math Jussieu 4:553–637, 2005).

中文翻译：

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同量异位自同构表示的合理性：CM 情况


在本文中，我们证明了作者与 M. Harris 联合结果对 Rankin-Selberg L 函数 $$L(s,\Pi \times \Pi ')$$L(s,Π×Π 临界值的联合结果的同时扩展′) (Grobner 和 Harris in J Inst Math Jussieu 15:711–769, 2016, Thm. 3.9) 到 (i) 一般 CM 域 F 和 (ii) 上同调自同构表示 $$\Pi '=\Pi _1\boxplus \cdots \boxplus \Pi _k$$Π′=Π1⊞⋯⊞Πk 是 F 上任意秩的一般线性群的酉尖头自守表示 $$\Pi _i$$Πi 的等压和。在这个意义上，这些注释的主要结果，参见。定理 1.9 是 Raghuram 主要结果的概括和补充（Forum Math 28:457–489, 2016；Int Math Res Not 2:334–372, 2010。https://doi.org/ 10.1093/imrn/rnp127) 和 Mahnkopf (J Inst Math Jussieu 4:553–637, 2005)。