Zeros of Hook Polynomials and Related Questions - Bridges, Walter; Craig, William; Folsom, Amanda; Rolen, Larry (Symmetry, Integrability and Geometry: Methods and Applications, 2025)
We study the zero set of polynomials built from partition statistics, complementing earlier work in this direction by Boyer, Goh, Parry, and others. In particular, addressing a question posed by Males, two of the authors prove asymptotics for the values of -hook polynomials away from an annulus and at isolated zeros of a theta function. We also discuss some open problems and present data on other polynomial families, including those associated with deformations of Rogers-Ramanujan functions.