The growth of entire functions of genus zero

2006/10/01 by Dang Duc Trong, Trong, Dang Duc, Truong Trung Tuyen +1
Mathematics · #30C85 #30D15 #31A15 #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.math/0610045

openalex publication_date 2006/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we shall consider the assymptotic growth of |P_n(z)|^1/k_n where P_n(z) is a sequence of entire functions of genus zero. Our results extend a result of J. Muller and A. Yavrian. We shall prove that if the sequence of entire functions has a geometric growth at each point in a set E being non-thin at ∞ then it has a geometric growth in \CC also. Moreover, if E has some more properties, a similar result also holds for a more general kind of growth. Even in the case where P_n are polynomials, our results are new in the sense that it does not require k_n\succeq deg(P_n) as usually required.

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