A Siegel-Weil formula for $(U(1,1), U(V))$ over a function field with $\dim V$ greater than 2

TL;DR

This paper proves a Siegel-Weil formula for a dual pair of unitary groups over a function field, specifically for hermitian spaces of dimension greater than 2, expanding the understanding of automorphic forms in this setting.

Contribution

It establishes a new Siegel-Weil formula for the dual pair $(U(1,1), U(V))$ over a function field with $ ext{dim } V > 2$, extending previous results to higher-dimensional hermitian spaces.

Findings

Proves the Siegel-Weil formula in the specified setting.

Connects automorphic forms and theta series over function fields.

Provides a foundation for further research in automorphic representations over function fields.

Abstract

We establish a Siegel-Weil formula for the dual pair $(U(1,1), U(V))$ over a function field, where $V$ is a hermitian space of dimension greater than 2.