Difference "abc" theorem for entire functions and Difference analogue of truncated version of Nevanlinna second main theorem

2024/05/10 by Rui-Chun Chen, Zhi‐Tao Wen, Chen, Rui-Chun +1
Mathematics · #30D20 #30D35 #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.06317

openalex publication_date 2024/05/10 · openalex created_date 2024/05/14 · openalex updated_date 2026/07/28

Abstract

In this paper, we focus on the difference analogue of the Stothers-Mason theorem for entire functions of order less than 1, which can be seen as difference abc theorem for entire functions. We also obtain the difference analogue of truncated version of Nevanlinna second main theorem which reveals that a subnormal meromorphic function f(z) such that Δf(z)\not≡ 0 cannot have too many points with long length in the complex plane. Both theorems depend on new definitions of the length of poles and zeros of a given meromorphic function in a domain. As for the application, we consider entire solutions of difference Fermat functional equations.

Related

• Nevanlinna theory for the difference operator
• Nevanlinna theory of the Askey-Wilson divided difference operator
• Difference Nevanlinna theories with vanishing and infinite periods
• Mason's theorem with a difference radical
• A lemma on the difference quotients