The Second Main Theorem Concerning Small Algebroid Functions

TL;DR

This paper establishes a second main theorem for small algebroid functions, expanding the theoretical framework of value distribution theory for algebroid functions.

Contribution

It introduces the concept of meromorphic function elements and algebroid mappings, and proves a second main theorem for v-valued small algebroid functions.

Findings

Defined meromorphic function elements and algebroid mappings

Constructed a closed algebraic family of algebroid functions

Proved the second main theorem for v-valued small algebroid functions

Abstract

In this paper, we firstly give the definition of meromorphic function element and algebroid mapping. We also construct the algebroid function family in which the arithmetic, differential operations is closed. On basis of these works, we firstly proved the Second Main Theorem concerning small algebroid functions for v-valued algebroid functions.