Quasiautomorphic forms are isomorphic to vector-valued automorphic forms
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866916031159599104 |
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| author | Henry, Michael Andrew |
| author_facet | Henry, Michael Andrew |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_21067 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasiautomorphic forms are isomorphic to vector-valued automorphic forms Henry, Michael Andrew Number Theory 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. |
| title | Quasiautomorphic forms are isomorphic to vector-valued automorphic forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2605.21067 |