Free algebras of modular forms on ball quotients
In this paper, we study algebras of modular forms on unitary groups of signature (n, 1). We give a necessary and sufficient condition for an algebra of unitary modular forms to be free in terms of the modular Jacobian. As a corollary, we obtain a criterion that guarantees in many cases that, if L is...
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| Hauptverfasser: | , |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
29 August 2025
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| In: |
Research in the mathematical sciences
Year: 2025, Jahrgang: 12, Heft: 3, Pages: 1-47 |
| ISSN: | 2197-9847 |
| DOI: | 10.1007/s40687-025-00538-2 |
| Online-Zugang: | Resolving-System, kostenfrei, Volltext: https://doi.org/10.1007/s40687-025-00538-2
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| Verfasserangaben: | Haowu Wang and Brandon Williams |
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| 520 | |a In this paper, we study algebras of modular forms on unitary groups of signature (n, 1). We give a necessary and sufficient condition for an algebra of unitary modular forms to be free in terms of the modular Jacobian. As a corollary, we obtain a criterion that guarantees in many cases that, if L is an even lattice with complex multiplication and the ring of modular forms for its orthogonal group is a polynomial algebra, then the ring of modular forms for its unitary group is also a polynomial algebra. We prove that a number of rings of unitary modular forms are freely generated by applying these criteria to Hermitian lattices over the rings of integers of $$\mathbb {Q}(\sqrt{d})$$for $$d=-1,-2,-3$$. As a byproduct, our modular groups provide many explicit examples of finite-covolume reflection groups acting on complex hyperbolic space. | ||
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| 650 | 4 | |a Complex reflection groups | |
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| 650 | 4 | |a Unitary modular forms | |
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