Prime detecting quasi-modular forms in higher level
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910224158294016 |
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| author | Kane, Ben Krishnamoorthy, Krishnarjun Lau, Yuk-Kam |
| author_facet | Kane, Ben Krishnamoorthy, Krishnarjun Lau, Yuk-Kam |
| contents | In a previous work, the authors resolved a conjecture about the structure of prime-detecting quasi-modular forms by studying sign changes occurring in quasi-modular cusp forms. In this paper, we extend the considerations to prime-detecting quasi-modular forms of higher level, in particular describing the structure of the space of quasi-modular forms that detect primes in various arithmetic progressions. We also provide an ``analytic'' proof of the level one case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04030 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prime detecting quasi-modular forms in higher level Kane, Ben Krishnamoorthy, Krishnarjun Lau, Yuk-Kam Number Theory 11F11, 11F30 In a previous work, the authors resolved a conjecture about the structure of prime-detecting quasi-modular forms by studying sign changes occurring in quasi-modular cusp forms. In this paper, we extend the considerations to prime-detecting quasi-modular forms of higher level, in particular describing the structure of the space of quasi-modular forms that detect primes in various arithmetic progressions. We also provide an ``analytic'' proof of the level one case. |
| title | Prime detecting quasi-modular forms in higher level |
| topic | Number Theory 11F11, 11F30 |
| url | https://arxiv.org/abs/2511.04030 |