The Siegel-Weil formula for unitary groups: the second term range

TL;DR

This paper investigates the Siegel-Weil formula within the second term range for unitary groups over hermitian forms on skew-fields, expanding understanding of automorphic forms and representation theory in this context.

Contribution

It extends the Siegel-Weil formula to the second term range for unitary groups over skew-fields with involution of the second kind, a previously less understood area.

Findings

Established the formula in the second term range for specified unitary groups.

Provided new insights into automorphic forms associated with these groups.

Enhanced the theoretical framework for hermitian forms over skew-fields.

Abstract

We study the Siegel-Weil formula in the second term range ($n+1\leq m\leq n+r$) for unitary groups of hermitian forms over a skew-field $D$ with involution of the second kind.