Difference analogue of Cartan's Second Main Theorem for slowly moving periodic targets

TL;DR

This paper extends the difference analogue of Cartan's Second Main Theorem to slowly moving periodic targets, introduces new approaches for difference analogues of the truncated theorem, and derives applications like Picard type theorems and deficiency relations.

Contribution

It provides novel extensions of the difference analogue of Cartan's Second Main Theorem for slowly moving targets and introduces two methods for difference analogues of the truncated theorem.

Findings

New Picard type theorem for holomorphic curves.

Difference analogues of deficiency relations.

Extended second main theorem for slowly moving hyperplanes.

Abstract

We extend the difference analogue of Cartan's second main theorem for the case of slowly moving periodic hyperplanes, and introduce two different natural ways to find a difference analogue of the truncated second main theorem. As applications, we obtain a new Picard type theorem and difference analogues of the deficiency relation for holomorphic curves.