A note on the value distribution of f^l(f^(k))ⁿ

2014/05/15 by Jiang Yan, Yan, Jiang, Bin, Huang
Mathematics · #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematics and Applications #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1405.3742

openalex publication_date 2014/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a transcendental meromorphic function in the complex plane ℂ, and a be a nonzero complex number . We give quantitative estimates for the characteristic function T(r,f) in terms of N(r,1/(f^l(f^(k))ⁿ-a)), for integers k, l, n greater than 1. We conclude that f^l(f^(k))ⁿ assumes every nonzero finite value infinitely often.

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