Abstract:
We prove an algebraicity result for all the critical values of L-functions for
GL3 × GL1 over a totally real field, and a CM field separately. These L-
functions are attached to a cohomological cuspidal automorphic representation
of GL3 having cohomology with respect to a general coefficient system
and an algebraic Hecke character of GL1. This is derived from the theory of
Rankin{Selberg L-functions attached to pairs of automorphic representations
on GL3 × GL2. Our results are a generalization and refinement of the results
of Mahnkopf [26] and Geroldinger [14]. The resulting expressions for critical
values of the Rankin-Selberg L-functions are compatible with Deligne's
conjecture. As an application, we obtain algebraicity results for symmetric
square L-functions.
