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A simple proof of Zagier duality for Hilbert modular forms

Author(s): D. Choi
Journal: Proc. Amer. Math. Soc. 134 (2006), 3445-3447.
MSC (2000): Primary 11F11; Secondary 11F41
Posted: June 9, 2006
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Abstract: In this paper, we give a simple proof of an identity between the Fourier coefficients of the weakly holomorphic modular forms of weight 0 arising from Borcherds products of Hilbert modular forms and those of the weakly holomorphic modular forms of weight satisfying a certain property.

References:

1.: J. H. Bruinier and M. Bundschuh, On Borcherds products associated with lattices of prime discriminant. Rankin memorial issues, Ramanujan J. 7 (2003), no. 1-3, 49-61. MR 2035791 (2005a:11057)
2.: J. Rouse, Zagier duality for the exponents of Borcherds products for Hilbert modular forms, to appear in Journal of the London Mathematical Society.

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Additional Information:

D. Choi
Affiliation: Department of Mathematics, Pohang University of Science and Technology, Pohang, 790--784, Korea
Address at time of publication: School of Mathematics, KIAS, 207-43 Cheongnyangni 2-dong, Seoul, 130-722, Korea
Email: choija@postech.ac.kr

DOI: 10.1090/S0002-9939-06-08440-1
PII: S 0002-9939(06)08440-1
Keywords: Modular forms, Hilbert modular forms
Received by editor(s): June 8, 2005
Received by editor(s) in revised form: July 3, 2005
Posted: June 9, 2006
Additional Notes: This work was partially supported by KOSEF R01-2003-00011596-0.
Communicated by: Ken Ono
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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