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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)
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.