  We prove a generalization to the totally real field case of the Waldspurger's
formula relating the Fourier coefficient of a half integral weight form and the
central value of the L-function of an integral weight form. Our proof is based
on a new interpretation of Waldspurger's formula in terms of equality between
global distributions. As applications we generalize the Kohnen-Zagier formula
for holomorphic forms and prove the equivalence of the Ramanujan conjecture for
half integral weight forms and a case of the Lindelof hypothesis for integral
weight forms. We also study the Kohnen space in the adelic setting.
