Special Correspondences of CM Abelian Varieties and Eisenstein Series II

TL;DR

This paper establishes a connection between special geometric cycles on certain Shimura varieties and the derivatives of Hilbert Eisenstein series, advancing understanding in arithmetic geometry and automorphic forms.

Contribution

It proves a new relation between special cycles on Shimura varieties and derivatives of Eisenstein series, extending previous work in the field.

Findings

Established a relation between special cycles and Eisenstein series derivatives

Extended the theory to Rapoport-Smithling-Zhang Shimura varieties

Provided new insights into automorphic forms and arithmetic geometry

Abstract

In this paper, we prove the relation between special cycles on a Rapoport-Smithling-Zhang Shimura variety and special values of the derivative of a Hilbert Eisenstein series.