Zero Distribution of Polynomials Generated by a Power of a Cubic Polynomial

2025/04/29 by Steele, Travis, Khang Tran, Tran, Khang
Mathematics · #11C08 #26C10 #30C15 #Analytic Number Theory Research #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2504.20374

openalex publication_date 2025/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For each α>0 and A(z),B(z)∈ℂ[z], we study the zero distribution of the sequence of polynomials \ P_m^(α)(z)\ _m=0^∞ generated by (1+B(z)t+A(z)t³)^-α. We show that for large m, the zeros of P_m^(α)(z) lie on an explicit curve on the complex plane.

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