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TRACES OF SINGULAR VALUES AND BORCHERDS PRODUCTS

Published online by Cambridge University Press:  20 September 2006

CHANG HEON KIM
CHANG HEON KIM
Affiliation:
Department of Mathematics, Seoul Women's University, 126 Kongnung 2-dong Nowongu, Seoul 139-774, South [email protected]
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Abstract

Let $p$ be a prime for which the congruence group $\Gamma_0(p)^*$ is of genus zero, and let $j_p^*$ be the corresponding Hauptmodul. Let $f$ be a nearly holomorphic modular form of weight 1/2 on $\Gamma_0(4p)$ which satisfies some congruence condition on its Fourier coefficients. We interpret $f$ as a vector valued modular form. Applying Borcherds lifting of vector valued modular forms we construct infinite products associated to $j_p^*$ and relate them to Zagier's trace formula for the singular values of $j_p^*$.

Keywords

11F0311F30 (primary)11F2211F3711F50 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 5 , October 2006 , pp. 730 - 740
Copyright
© The London Mathematical Society 2006

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Footnotes

This paper was supported by the Natural Science Research Institute of Seoul Women's University, 2004.