Ichino–Ikeda–N. Harris conjecture for unitary groups
Ichino–Ikeda–N. Harris conjecture for unitary groups
Let and be factorizable vectors in representations and , respectively. Let be the period pairing, the global arithmetic factor, \c the partial -value, and the normalized local integral at each place in a finite set . Ichino–Ikeda–N. Harris conjecture. There is an integer , depending on the -packets containing and , 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 -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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