The generating function for traces of singular moduli and an application to Borcherds products

Let p be a prime and f (z) = Sigma(n) a(n)q(n) be a weakly holomorphicmodular function for Gamma(0)*(p(2)) with a(0) = 0. We use Bruinier and Funke's work to find the generating series of modular traces of f (z) as Jacobi forms. And as an application we construct Borcherds products related to the Hauptmoduln j(p2)* for genus zero groups Gamma(0)*(p(2)).