Higher Schwarzian, quasimodular forms and equivariant functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909493474885632 |
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| author | Saber, Hicham Sebbar, Abdellah |
| author_facet | Saber, Hicham Sebbar, Abdellah |
| contents | The Schwarzian derivative plays a fundamental role in complex analysis, differential equations, and modular forms. In this paper, we investigate its higher-order generalizations, known as higher Schwarzians, and their connections to quasimodular forms and equivariant functions. We prove that a meromorphic function is equivariant if and only if its higher Schwarzians are quasimodular forms of prescribed weight and depth, thereby extending classical results and linking projective differential operators to the structure of modular and quasimodular forms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_10176 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher Schwarzian, quasimodular forms and equivariant functions Saber, Hicham Sebbar, Abdellah Number Theory Mathematical Physics Classical Analysis and ODEs The Schwarzian derivative plays a fundamental role in complex analysis, differential equations, and modular forms. In this paper, we investigate its higher-order generalizations, known as higher Schwarzians, and their connections to quasimodular forms and equivariant functions. We prove that a meromorphic function is equivariant if and only if its higher Schwarzians are quasimodular forms of prescribed weight and depth, thereby extending classical results and linking projective differential operators to the structure of modular and quasimodular forms. |
| title | Higher Schwarzian, quasimodular forms and equivariant functions |
| topic | Number Theory Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2502.10176 |