Kloosterman sums and traces of singular moduli Original Research Article

We give a new proof of some identities of Zagier relating traces of singular moduli to the coefficients of certain weakly holomorphic half integral weight modular forms. These identities play a central role in Zagierʹs work on the infinite product isomorphism introduced by Borcherds. In addition, we derive a simple expression for writing twisted traces of singular moduli as infinite series.