We derive for Hecke-Maass cusp forms on the full modular group a relat
ion between the sum of the form st Heegner points (and integrals over
Heegner cycles) and the product of two Fourier coefficients of a corre
sponding form of half-integral weight. Specializing to certain cycles
we obtain the non-negativity of the L-function of such a form at the c
enter of the critical strip. These results generalize similar formulae
known for holomorphic forms.