On a conjecture about prime-detecting quasimodular forms
Number Theory
2025-07-10 v2
Abstract
Motivated by weighted partition of that vanish if and only if is a prime, Craig, van Ittersum, and Ono conjecture a classification of quasimodular forms which detect primes in the sense that the -th Fourier coefficient vanishes if and only if is a prime. In this paper, we prove this conjecture by showing that Fourier coefficients of quasimodular cusp forms exhibit infinitely many sign changes.
Cite
@article{arxiv.2507.00147,
title = {On a conjecture about prime-detecting quasimodular forms},
author = {Ben Kane and Krishnarjun Krishnamoorthy and Yuk-Kam Lau},
journal= {arXiv preprint arXiv:2507.00147},
year = {2025}
}