2014/01/22 by Risto Korhonen, Kazuya Tohge, Korhonen, Risto +1
Computer Science · Mathematics · #30D35 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation #Primary 14T05 #Secondary 32H30
paper · pdf · doi:10.48550/arxiv.1401.5584
openalex publication_date 2014/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Tropical Nevanlinna theory, introduced by Halburd and Southall as a tool to analyze integrability of ultra-discrete equations, studies the growth and complexity of continuous piecewise linear real functions. The purpose of this paper is to extend tropical Nevanlinna theory to n-dimensional tropical projective spaces by introducing a natural characteristic function for tropical holomorphic curves, and by proving a tropical analogue of Cartan's second main theorem. It is also shown that in the 1-dimensional case this result implies a known tropical second main theorem due to Laine and Tohge.