Work

Zeros of Hook Polynomials and Related Questions

Year: 2025

Type: article

Abstract: 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 of Males with two of the authors, we prove asymptotics for the values of $t$-hook polynomials away from an annulus and isolated zeros of a theta function. We also discuss some open problems and present data on other polynomial families, including those associated to deformations of Rogers-Ramanujan functions.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2025.026

Authors: Walter Bridges, William Craig, Amanda Folsom, Larry Rolen

Institutions: University of North Texas, United States Naval Academy, Amherst College, Vanderbilt University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Science Foundation, U.S. Department of Defense, U.S. Navy, U.S. Naval Academy

Award: RUI: Harmonic Maass Forms and Quantum Modular Forms