Title: Integral traces of singular values of Maass forms

Abstract: In this joint work with W. Duke, we define traces associated to a weakly holomorphic modular form f of negative even integral weight and show that these traces appear as coefficients of certain weakly holomorphic modular forms of half-integral weight. If the coefficients of f are integral, then these traces are integral as well. We obtain a negative weight analogue of the classical Shintani lift, and give a natural generalization of the Shimura lift.