ZAGIER DUALITY FOR THE EXPONENTS OF BORCHERDS PRODUCTS FOR HILBERT MODULAR FORMS

A certain sequence of weight 1/2 modular forms arises in the theory of Borcherds products for modular forms for SL2(Z). Zagier proved a family of identities between the coefficients of these weight 1/2 forms and a similar sequence of weight 3/2 modular forms, which interpolate traces of singular moduli. We obtain the analogous results for modular forms arising from Borcherds products for Hilbert modular forms.