Tropical variants of some complex analysis results
Kai Liu, Ilpo Laine, Kazuya Tohge
TL;DR
This paper applies tropical Nevanlinna theory to develop tropical analogues of classical complex analysis results, focusing on value distribution and related conjectures.
Contribution
It introduces tropical counterparts of key complex analysis theorems related to Fermat equations, Hayman, and Bruck conjectures, expanding tropical analysis.
Findings
Tropical Nevanlinna theory provides a framework for value distribution of piecewise linear functions.
Classical results like Fermat type equations are extended into the tropical setting.
New tropical analogues of Hayman and Bruck conjectures are established.
Abstract
Tropical Nevanlinna theory studies value distribution of continuous piecewise linear functions of a real variable. In this paper, we use the reasoning from tropical Nevanlinna theory to present tropical counterparts of some classical complex results related to Fermat type equations, Hayman conjecture and Bruck conjecture.
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Taxonomy
TopicsMeromorphic and Entire Functions · Advanced Differential Equations and Dynamical Systems