摘要
The aim of this article is to prove the Siegel-Weil formula over function fields for the dual reductive pair (Sp n , O(V)), where Sp n is the symplectic group of degree 2n and (V, QV) is an anisotropic quadratic space with even dimension. This is a function field analogue of Kudla and Rallis' result. By this formula, the theta series is identified with the special value of the Siegel- Eisenstein series on Sp n at a critical point.