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

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.