On a conjecture about prime-detecting quasimodular forms
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911046393921536 |
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| author | Kane, Ben Krishnamoorthy, Krishnarjun Lau, Yuk-Kam |
| author_facet | Kane, Ben Krishnamoorthy, Krishnarjun Lau, Yuk-Kam |
| contents | Motivated by weighted partition of $n$ that vanish if and only if $n$ is a prime, Craig, van Ittersum, and Ono conjecture a classification of quasimodular forms which detect primes in the sense that the $n$-th Fourier coefficient vanishes if and only if $n$ is a prime. In this paper, we prove this conjecture by showing that Fourier coefficients of quasimodular cusp forms exhibit infinitely many sign changes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_00147 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a conjecture about prime-detecting quasimodular forms Kane, Ben Krishnamoorthy, Krishnarjun Lau, Yuk-Kam Number Theory 11F11, 11F30 Motivated by weighted partition of $n$ that vanish if and only if $n$ is a prime, Craig, van Ittersum, and Ono conjecture a classification of quasimodular forms which detect primes in the sense that the $n$-th Fourier coefficient vanishes if and only if $n$ is a prime. In this paper, we prove this conjecture by showing that Fourier coefficients of quasimodular cusp forms exhibit infinitely many sign changes. |
| title | On a conjecture about prime-detecting quasimodular forms |
| topic | Number Theory 11F11, 11F30 |
| url | https://arxiv.org/abs/2507.00147 |