Ichino–Ikeda–N. Harris conjecture for unitary groups

Let \f\f and \f\f' be factorizable vectors in representations 0¸\c0 and 0¸\c0', respectively. Let \a\a be the period pairing, b{\overline{\frak b}} the global arithmetic factor, \c the partial LL-value, and \d\d the normalized local integral at each place vv in a finite set SS. Ichino–Ikeda–N. Harris conjecture. There is an integer b{\overline{\frak b}}, depending on the LL-packets containing 0¸\c0 and 0¸\c0', such that

\a(\f,\f')=2^{{\overline{\frak b}}}{\overline{\frak b}}\c\prod_{v\in S}\d_v(\f_v,\f'_v).

This formula relates the square of a global period to a product of local periods and an automorphic LL-value; the candidate is presented in the source as a conjectural Ichino–Ikeda formula, and no resolution is supplied in the provided text.

Sources & referencesView supporting material

Primary source

Michael Harris, “Square root p-adic L-functions, I: Construction of a one-variable measure”, arXiv:1911.01925 (2020).

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