WALDSPURGER FORMULA OVER FUNCTION FIELDS.

In this paper, we derive a function field version of theWaldspurger formula for the central critical values of the Rankin-Selberg L-functions. This formula states that the central critical L-values in question can be expressed as the "ratio" of the global toric period integral to the product of the local toric period integrals. Consequently, this result provides a necessary and sufficient criterion for the non-vanishing of these central critical L-values, and supports the Gross-Prasad conjecture for SO(3) over function fields. [ABSTRACT FROM AUTHOR]