Unconditional proof that Λ(s,R)=Λ(1−s,R) for Gorenstein orders R in cubic fields, rendering Deng–Espinosa’s isolation of the trivial representation for GL3(Q) fully unconditional.
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Beyond Endoscopy for $\mathrm{GL}_3(\mathbb{Q})$: Functional equation for the $L$-function of a cubic order
Unconditional proof that Λ(s,R)=Λ(1−s,R) for Gorenstein orders R in cubic fields, rendering Deng–Espinosa’s isolation of the trivial representation for GL3(Q) fully unconditional.