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Journal of the London Mathematical Society 2006 73(2):339-354; doi:10.1112/S0024610706022642
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© The London Mathematical Society

Zagier Duality for the Exponents of Borcherds Products for Hilbert Modular Forms

Jeremy Rouse

Department of Mathematics, University of Wisconsin 480 Lincoln Drive, Madison, WI 53706, USA rouse{at}math.wisc.edu

Received 14 February 2005. Revision received 28 June 2005.

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.


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