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28 March 2024
 
  » arxiv » math.NT/0305183

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Traces of singular values and Borcherds products
Chang Heon Kim ;
Date 13 May 2003
Subject Number Theory MSC-class: Primary 11F03, 11F30; Secondary 11F22, 11F37, 11F50 | math.NT
AbstractLet $p$ be a prime for which the congruence group $Gamma_0(p)^*$ is of genus zero, and $j_p^*$ 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 extend Zagier’s trace formula for singular values of $j_p^*$. Further we investigate the twisted traces of sigular values of $j_p^*$ and construct Borcherds products related to them.
Source arXiv, math.NT/0305183
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