Geodesic
Eisenstein Cohomology for $\mathrm {GL}_N$ and the special values of Rankin–Selberg L-functions over a totally imaginary number field
Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e86

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This article presents new rationality results for the ratios of critical values of Rankin–Selberg L-functions of $\mathrm {GL}(n) \times \mathrm {GL}(n')$ over a totally imaginary field $F.$ The proof is based on a cohomological interpretation of Langlands’s contant term theorem via rank-one Eisenstein cohomology for the group $\mathrm {GL}(N)/F,$ where $N = n+n'.$ The internal structure of the totally imaginary base field has a delicate effect on the Galois equivariance properties of the critical values. 
Raghuram, A. Eisenstein Cohomology for $\mathrm {GL}_N$ and the special values of Rankin–Selberg L-functions over a totally imaginary number field. Forum of Mathematics, Sigma, Tome 13 (2025) no. 1, p. e86. doi: 10.1017/fms.2025.48
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