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# Asian Journal of Mathematics

## Volume 19 (2015)

### Number 3

### On the Siegel–Weil formula over function fields

Pages: 487 – 526

DOI: http://dx.doi.org/10.4310/AJM.2015.v19.n3.a5

#### Author

#### Abstract

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