Traces of singular values and Borcherds products

الأصل · EN

Let p be a prime for which the congruence group Γ₀(p)* is of genus zero, and 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 extend Zagier's trace formula for singular values of jₚ*. Further we investigate the twisted traces of sigular values of jₚ* and construct Borcherds products related to them.