A new regularized Siegel-Weil type formula, part I

TL;DR

This paper introduces a novel regularized Siegel-Weil type formula connecting residues of Eisenstein series on symplectic groups, extending previous work by Kudla-Rallis and others, with potential implications for automorphic forms.

Contribution

It proposes a new formula relating residues of Eisenstein series on symplectic groups, inspired by and similar to the classical Siegel-Weil formula, extending prior generalizations.

Findings

Proposed a new regularized formula for Eisenstein series residues

Established connections to classical Siegel-Weil formula

Extended previous generalizations by Kudla-Rallis and others

Abstract

In this paper, we propose a formula relating certain residues of Eisenstein series on symplectic groups. These Eisenstein series are attached to parabolic data coming from Speh representations. The proposed formula bears a strong similarity to the regularized Siegel-Weil formula, established by Kudla and Rallis for symplectic-orthogonal dual pairs. Their work was later generalized by Ikeda, Moeglin, Ichino, Yamana, Gan-Qiu-Takeda and others.