Special values of automorphic L-functions for GL(2n)

I will begin my talk with Shimura's theorem on the critical values of the standard L-function attached to a holomorphic Hilbert modular form. Then, I will recast Shimura's theorem into a more representation-theoretic context by talking about the critical values of L-functions attached to cohomological cuspidal automorphic
representations for GL(2) over a totally real number field F. The second part of my talk will be about my
recent joint work with Harald Grobner concerning the critical values of L-functions attached to
cohomological cuspidal automorphic representations of GL(2n) over F which admit Shalika models. Putting
n=1 retrieves Shimura's theorem. These results provide a new theorem/proof for the critical values of
the third symmetric power L-function of a Hilbert modular form.