Congruences between Klingen-Eisenstein series and cusp forms on $\mathrm{U}_{n,n}$

TL;DR

This paper investigates congruences of Hecke eigenvalues between Hermitian Klingen-Eisenstein series and cusp forms on the unitary group U_{n,n}, establishing rationality and integrality properties of automorphic forms.

Contribution

It proves the rationality of the space of Hermitian automorphic forms and the integrality of their Hecke eigenvalues, advancing understanding of automorphic forms on unitary groups.

Findings

Proved rationality of Hermitian automorphic form space

Established integrality of Hecke eigenvalues

Analyzed congruences between Eisenstein series and cusp forms

Abstract

In this paper, we study congruences of Hecke eigenvalues between Hermitian Klingen-Eisenstein series and cusp forms on the unitary group $\mathrm{U}_{n,n}$ defined over the rational number field $\mathbb{Q}$. We also prove the rationality of the space of Hermitian automorphic forms and the integrality of their Hecke eigenvalues.