On the Siegel–Weil formula over function fields

The aim of this article is to prove the Siegel-Weil formula over function fields for the dual reductive pair $(\mathrm{Sp}_n, \mathrm{O}(V))$, where $\mathrm{Sp}_n$ is the symplectic group of degree $2n$ and $(V,Q_V)$ 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 $\mathrm{Sp}_n$ at a critical point.

Keywords

function field, theta series, Eisenstein series, automorphic form

2010 Mathematics Subject Classification

11F27, 11F55, 11M36, 11R58

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Published 19 June 2015