Subregular Fourier-coefficient conjecture for relevant unitary Arthur packets

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Let Gn=Un+1,n−1G_n={\mathrm {U}}_{n+1,n-1} be defined over FF with FF-rank n−1n-1, and let Gn∗=Un,nG_n^*={\mathrm {U}}_{n,n}. Let ϕ\phi be a generic global Arthur parameter of Gn∗G_n^* that is GnG_n-relevant, meaning that the global Arthur packet Π~ϕ(Gn)\widetilde{\Pi}_\phi(G_n) is nonempty. Let p‾=[(2n−1)1]\underline{p}=[(2n-1)1] be the partition corresponding to the FF-stable subregular unipotent orbit. Subregular Fourier-coefficient conjecture. There exists an automorphic member π0\pi_0 in Π~ϕ(Gn)\widetilde{\Pi}_\phi(G_n) with a nonzero Fourier coefficient associated to p‾\underline{p}. This conjecture supplies the refined packet property needed to extend the paper's non-vanishing results from low-rank quasisplit groups to the general situation.

References

Primary source

Dihua Jiang and Lei Zhang, “On the Non-vanishing of the Central Value of Certain L-functions: Unitary Groups”, arXiv:1806.04340 (2018).

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