Automatic convergence for holomorphic modular forms

TL;DR

This paper establishes an automatic convergence theorem for holomorphic modular forms on tube domains, applicable to various classical and exceptional groups, enhancing understanding of their analytic properties.

Contribution

It introduces a general automatic convergence theorem for holomorphic modular forms on tube domains, covering a wide range of groups including orthogonal, symplectic, unitary, quaternionic, and exceptional groups.

Findings

Proves an automatic convergence theorem for holomorphic modular forms.

Applicable to classical and exceptional groups.

Enhances understanding of modular forms' analytic behavior.

Abstract

We prove an automatic convergence theorem for holomorphic modular forms on tube domains. The argument works in some generality, and covers in particular the case of orthogonal groups, symplectic groups, unitary and quaternion unitary groups, and the exceptional group $E_7$.