On a conjecture about prime-detecting quasimodular forms
Abstract Motivated by weighted partitions of n that vanish if and only if n is a prime, Craig, van Ittersum, and Ono conjectured 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.
Authors
- Ben Kane
- Yuk-Kam Lau (ORCID: https://orcid.org/0000-0003-2765-5392)
- Krishnarjun Krishnamoorthy (ORCID: https://orcid.org/0000-0003-0837-7104)
Institutions
- Shandong University (CN)
- Chinese Mathematical Society (CN)
- University of Hong Kong (HK)
Publication Details
- Journal
- Research in the Mathematical Sciences
- Published
- 2025-08-25
- DOI
- https://doi.org/10.1007/s40687-025-00541-7
- Primary Topic
- Advanced Algebra and Geometry
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Natural Science Foundation of China
- University Grants Committee