Proofs of some conjectures by Bringmann, Han, Heim, and Kane on periodic sign changes in eta-quotients
Year: 2026
Type: preprint
Abstract: Bringmann, Han, Heim, and Kane recently investigated periodic sign patterns in the Fourier coefficients of weakly holomorphic modular forms arising from eta-quotients and posed numerous conjectures in the appendix to their work. Using classical theta-function identities, dissections, and coefficientwise positivity, we prove 72 of these conjectural sign patterns. The eta-quotients considered here have periods 2, 3, 4, 5, 6, 8, and 12. Our proofs are elementary at the level of $q$-series and yield explicit generating functions for the coefficients in each relevant residue class.
Source: arXiv (Cornell University)
Authors: Jin, Jing, Yao, Olivia X. M., Zhou, Shiwen
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Government of Jiangsu Province
OpenAlex ID: W7214988096