The weight-4 Gross-Zagier conjecture is reduced to Beilinson-Hodge and proved cycle-theoretically for 18 (conjecturally 23) genus-zero K3 mirror families.
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A note on higher Green's functions
The weight-4 Gross-Zagier conjecture is reduced to Beilinson-Hodge and proved cycle-theoretically for 18 (conjecturally 23) genus-zero K3 mirror families.