Quasiautomorphic forms are isomorphic to vector-valued automorphic forms

Michael Andrew Henry

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arXiv · 2605.21067

Quasiautomorphic forms are isomorphic to vector-valued automorphic forms

Michael Andrew Henry

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Abstract

We utilize the structure of quasiautomorphic forms over a Hecke triangle group to define a mapping from a quasiautomorphic form to a vector-valued automorphic form (vvaf). This kind of vvaf we call a Hecke vector-form. First we supply a proof of the functional equations that hold for Hecke vector-forms modulo the group generators. Then, utilizing the multiplier system for these Hecke vector-forms, we prove the opposite direction and complete the bijection. Since the modular group is a special instance of the Hecke triangle groups, our results hold for quasimodular forms.

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Michael Andrew Henry. 2026-05-20. Quasiautomorphic forms are isomorphic to vector-valued automorphic forms. https://arxiv.org/abs/2605.21067

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