Arithmetic properties of coefficients of half-integral weight Maass-Poincare series

Zagier [23] proved that the generating functions for the traces of level 1 singular moduli are weight 3/2 modular forms. He also obtained generalizations for "twisted traces", and for traces of special non-holomorphic modular functions. Using properties of Kloosterman-Salie sums, and a well known reformulation of Salie sums in terms of orbits of CM points, we systematically show that such results hold for arbitrary weakly holomorphic and cuspidal half-integral weight Poincare series in Kohnen's Gamma(0)(4) plus-space. These results imply the aforementioned results of Zagier, and they provide exact formulas for such traces.