Some conjectures around magnetic modular forms
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910399651119104 |
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| author | Bönisch, Kilian Duhr, Claude Maggio, Sara |
| author_facet | Bönisch, Kilian Duhr, Claude Maggio, Sara |
| contents | We study a class of meromorphic modular forms characterised by Fourier coefficients that satisfy certain divisibility properties. We present new candidates for these so-called magnetic modular forms, and we conjecture properties that these functions should obey. In particular, we conjecture that magnetic modular forms are closed under the standard operators acting on spaces of modular forms (SL$_2(\mathbb{Z})$ action, Hecke and Atkin-Lehner operators), and that they are characterised by algebraic residues and vanishing period polynomials. We use our conjectures to construct examples of real-analytic modular forms with poles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some conjectures around magnetic modular forms Bönisch, Kilian Duhr, Claude Maggio, Sara Number Theory We study a class of meromorphic modular forms characterised by Fourier coefficients that satisfy certain divisibility properties. We present new candidates for these so-called magnetic modular forms, and we conjecture properties that these functions should obey. In particular, we conjecture that magnetic modular forms are closed under the standard operators acting on spaces of modular forms (SL$_2(\mathbb{Z})$ action, Hecke and Atkin-Lehner operators), and that they are characterised by algebraic residues and vanishing period polynomials. We use our conjectures to construct examples of real-analytic modular forms with poles. |
| title | Some conjectures around magnetic modular forms |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.04085 |