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.