Result: Zeros of Hook Polynomials and Related Questions: Zeros of hook polynomials and related questions

Title:
Zeros of Hook Polynomials and Related Questions: Zeros of hook polynomials and related questions
Authors:
Bridges, Walter, Craig, William, Folsom, Amanda, Rolen, Larry
Source:
Symmetry, Integrability and Geometry: Methods and Applications.
Publication Status:
Preprint
Publisher Information:
SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 2025.
Publication Year:
2025
Subject Terms:
Combinatorial aspects of partitions of integers, zeros of polynomials, Mathematics - Number Theory, Exact enumeration problems, generating functions, theta functions, hook length, integer partitions, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), zero attractor, FOS: Mathematics, Mathematics - Combinatorics, Analytic theory of partitions, Theta series, Weil representation, theta correspondences, asymptotic behavior, Combinatorics (math.CO), Number Theory (math.NT)
Document Type:
Academic journal Article
File Description:
application/xml
ISSN:
1815-0659
DOI:
10.3842/sigma.2025.026
DOI:
10.48550/arxiv.2408.16902
Access URL:
http://arxiv.org/abs/2408.16902
https://zbmath.org/8035728
https://doi.org/10.3842/sigma.2025.026
Rights:
CC BY SA
Accession Number:
edsair.doi.dedup.....d56fd636ef903897387ccdec2b8df10c
Database:
OpenAIRE

Further Information

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.