Tropical second main theorem and the Nevanlinna inverse problem

TL;DR

This paper extends tropical Nevanlinna theory by generalizing the second main theorem to noncontinuous functions and hypersurfaces, introduces a novel proof method, and solves the inverse problem for tropical meromorphic functions.

Contribution

It provides a generalized second main theorem for tropical functions without growth restrictions and offers a new, simpler proof approach, also solving the tropical inverse problem.

Findings

Generalized second main theorem for noncontinuous tropical functions

Novel proof method simplifies existing proofs

Solved the tropical Nevanlinna inverse problem

Abstract

A generalization of the second main theorem of tropical Nevanlinna theory is presented for noncontinuous piecewise linear functions and for tropical hypersurfaces without requiring a growth condition. The method of proof is novel and significantly more straightforward than previously known proofs. The tropical analogue of the Nevanlinna inverse problem is formulated and solved for tropical meromorphic functions and tropical hypersurfaces.