On a conjecture about prime-detecting quasimodular forms

2025/06/30 by Ben Kane, Kane, Ben, Krishnarjun Krishnamoorthy +3 · 2 citations
Mathematics · #11F11 #11F30 #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2507.00147

openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Quasimodular forms that detect primes are Eisenstein
• Integer partitions detect the primes

Cited by

• Prime detecting quasi-modular forms in higher level
• Quasimodular forms that detect primes are Eisenstein

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