#### Vol. 16, No. 5, 2022

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Entirety of certain cuspidal Eisenstein series on Kac–Moody groups

### Lisa Carbone, Kyu-Hwan Lee and Dongwen Liu

Vol. 16 (2022), No. 5, 1099–1119
##### Abstract

Let $G$ be an infinite-dimensional representation-theoretic Kac–Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We consider Eisenstein series on $G$ induced from unramified cusp forms on finite-dimensional Levi subgroups of maximal parabolic subgroups. Under a natural condition on maximal parabolic subgroups, we prove the cuspidal Eisenstein series are entire on the full complex plane.

##### Keywords
Eisenstein series, Kac–Moody groups, entirety
##### Mathematical Subject Classification
Primary: 11F70, 20G44