Tadashi Miyazaki

<p>After introducing the notion of uniform integrality of critical values of the Rankin–Selberg -functions for , we study it when the base field is totally imaginary. For this purpose, we adopt specific models with highest weight representations of the general linear groups, construct the Eichler–Shimura classes for and in an explicit manner, and then evaluate the cohomological cup product of them, by making the best use of Gel′fand–Tsetlin basis.</p>

<p>Let and be positive integers such that . Let be either or . Let and be maximal compact subgroups of and , respectively. We give the explicit descriptions of archimedean Rankin–Selberg integrals at the minimal - and -types for pairs of principal series representations of and , using their recurrence relations. Our results for can be applied to the arithmetic study of critical values of automorphic -functions.</p>