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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 | Abstract: | Let $p$ 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 | Services: | Forum | Review | PDF | Favorites |
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