Work

On a conjecture about prime-detecting quasimodular forms

Year: 2025

Type: article

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.

Source: Research in the Mathematical Sciences

DOI: 10.1007/s40687-025-00541-7

Authors: Ben Kane, Krishnarjun Krishnamoorthy, Yuk-Kam Lau

Institutions: University of Hong Kong, Beijing Institute of Mathematical Sciences and Applications, Shandong University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,090

Funders: National Natural Science Foundation of China, University Grants Committee