Non-real zeros of derivatives in the unit disc

2024/03/28 by James K. Langley, Langley, James
Mathematics · #30D35 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2403.19403

openalex publication_date 2024/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result establishes an estimate for the growth of a real meromorphic function f on the unit disc Δ such that: (i) at least one of f and 1/f has finitely many poles and non-real zeros in Δ; (ii)~f^(k) has finitely many non-real zeros in Δ, for some k ≥ 2.

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