Let p be a prime for which the congruence group Γ0(p)* is of genus zero, and let jp* 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 jp* and relate them to Zagier's trace formula for the singular values of jp*. 2000 Mathematics Subject Classification 11F03, 11F30 (primary); 11F22, 11F37, 11F50 (secondary).

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