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arxiv: math/0305183 · v2 · submitted 2003-05-13 · 🧮 math.NT

Traces of singular values and Borcherds products

classification 🧮 math.NT
keywords borcherdsmodularproductsvaluescongruenceconstructformgamma
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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.

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