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This is in continuation of my first talk on the same topic. In this talk, I will
present my recent work with Harald Grobnet on the special values of L-functions
for GL(2n) over a totally real number field F. Here the periods arise via a comparison of rational structures on Shalika models (if there is one at hand) and top-degree cuspidal cohomology. Results on L-values will follow by giving a
cohomological interpretation to certain zeta-integrals of Friedberg and Jacquet. Time and mood permitting, I will discuss the implications for classical L-functions like symmetric power L-functions oof a modular form, or the degree four
`Spinor' L-function of a genus-twi Siegel modular form. (Pre-requisites: First talk !
If F=Q and n=1, the situation is exactly as in the first talk.)
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