For ordinary automorphic forms on unitary groups U(r,s) over totally real fields, it proves that a rank-zero Selmer group forces the central L-value to be nonzero.
Wan, Families of nearly ordinary Eisenstein series o n unitary groups (with an Appendix by Kai-Wen Lan), Algebra and Number Theory (2015): 1955-2054
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Iwasawa theory for $\mathrm{U}(r,s)$, Bloch-Kato conjecture and Functional Equation
For ordinary automorphic forms on unitary groups U(r,s) over totally real fields, it proves that a rank-zero Selmer group forces the central L-value to be nonzero.