Traces of Singular Values and Borcherds Products

Let p be a prime for which the congruence group ₀(p)* is ofgenus zero, and let be the corresponding Hauptmodul. Let f be a nearly holomorphic modularform of weight 1/2 on ₀(4p) which satisfies some congruencecondition on its Fourier coefficients. We interpret f as a vectorvalued modular form. Applying Borcherds lifting of vector valuedmodular forms we construct infinite products associated to and relate them to Zagier's traceformula for the singular values of . 2000 Mathematics Subject Classification 11F03, 11F30 (primary);11F22, 11F37, 11F50 (secondary).