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Rationality results are proved for the ratios of critical values ofRankin-Selberg L-functions of GL(n) x GL(n') over a totally imaginary field F,by studying rank-one Eisenstein cohomology for the group GL(N)/F, where N =n+n', generalizing the methods and results of previous work with Guenter Harderwhere the base field was totally real. In contrast to the totally realsituation, the internal structure of the totally imaginary base field has adelicate effect on the rationality results.

Eisenstein Cohomology for GL(N) and the special values of Rankin-Selberg L-functions over a totally imaginary number field