Second Main Theorems of Jackson Difference Operator for Holomorphic Curves with Slowly Moving Targets

Abstract

In this paper, we investigate some new truncated second main theorems by using the Jackson \( p \)-Casorati determinant, where the truncated counting functions are assigned varying weights. We specifically concentrate on the Jackson difference operator applied to zero-order holomorphic mappings intersecting a finite set of slowly moving targets in \( \mathbb {P}^n(\mathbb {C}) \). As an application, we prove a uniqueness theorem of meromorphic functions sharing some small functions with the Jackson-type counting functions.