Second main theorems for meromorphic mappings and moving hyperplanes with truncated counting functions

TL;DR

This paper develops new second main theorems for meromorphic mappings into projective space with moving hyperplanes, improving previous results by incorporating truncated counting functions.

Contribution

It introduces refined second main theorems for meromorphic mappings with moving hyperplanes using truncated counting functions, advancing the theoretical framework.

Findings

Enhanced second main theorems with truncated counting functions

Improved bounds for meromorphic mappings and moving hyperplanes

Generalization of previous results in value distribution theory

Abstract

In this article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hyperplanes with truncated counting functions. Our results are improvements of the previous second main theorems for moving hyperplanes with truncated (to level $n$) counting functions.