On the Siegel-Weil formula for classical groups over function fields

TL;DR

This paper proves a Siegel-Weil formula for classical groups over function fields with odd characteristic, linking Eisenstein series and theta integrals, and provides a convergence criterion using Harder's reduction theory.

Contribution

It extends the classical Siegel-Weil formula to the setting of function fields with odd characteristic, including convergence criteria.

Findings

Established a Siegel-Weil formula for classical groups over function fields

Provided a convergence criterion for the theta integral using Harder's reduction theory

Connected Eisenstein series with theta functions in the function field context

Abstract

We establish a Siegel-Weil formula for classical groups over a function field with odd characteristic, which asserts in many cases that the Siegel Eisenstein series is equal to an integral of a theta function. This is a function-field analogue of the classical result proved by A. Weil in his 1965 Acta Math. paper. We also give a convergence criterion for the theta integral by using Harder's reduction theory over function fields.