Traces of Singular Values and Borcherds Products
نویسنده
چکیده
Abstract. Let p be a prime for which the congruence group Γ0(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 Γ0(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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