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

Published online by Cambridge University Press:  24 April 2006

JEREMY ROUSE
JEREMY ROUSE
Affiliation:
Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, WI 53706, USArouse@math.wisc.edu
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Abstract

A certain sequence of weight $1/2$ modular forms arises in the theory of Borcherds products for modular forms for $\textrm{SL}_{2}(\Z)$. 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.

Keywords

11F30 (primary)11F41 (secondary)

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Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 73 , Issue 2 , April 2006 , pp. 339 - 354
Copyright
The London Mathematical Society 2006

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Footnotes

This research was supported by the NDSEG Fellowship Program, which is sponsored by the Department of Defense and the Office of Naval Research.