n阶热带Nevanlinna理论
n-th Tropical Nevanlinna Theory
AI总结：
本文将热带Nevanlinna理论拓展到分段多项式连续函数，构造n阶Poisson-Jensen公式引入相关函数，推导两类第二基本定理并证明强等式，指出移位算子无自然热带截断型第二基本定理。
摘要：
本文将热带Nevanlinna理论拓展至分段多项式连续函数范畴。通过构造n阶Poisson-Jensen公式，引入了n阶热带计数函数、邻近函数与特征函数，这类函数与经典热带情形下的对应函数具备若干不同性质。随后，研究不仅得到了针对热带齐次多项式的n阶版本第二基本定理，还获得了针对普通费马型多项式的热带第二基本定理。此外，通过在逐点增长假设下估计热带对数导数，证明了一个强等式。该等式阐明了$\sum_{i=0}^{m}N(r, 1_{0}\oslash f_{i})$与分歧项$N(r, C_{0}(f_{0}, \cdots, f_{m}))$之间的关系，表明移位算子不存在自然的热带截断型第二基本定理。
英文摘要：
In this paper, the tropical Nevanlinna theory is extended for piecewise polynomial continuous functions. By constructing the $n$-th Poisson-Jensen formula, the $n$-th tropical counting, proximity, and characteristic functions are introduced, which have some different properties compared to the classical tropical setting. Then, not only is the $n$-th version of the second main theorem for tropical homogeneous polynomials obtained, but also a tropical second main theorem for ordinary Fermat type polynomials is acquired. Moreover, by estimating the tropical logarithmic derivative with a growth assumption pointwise, a strong equality is proved. This equality illustrates the relationship between $\sum_{i=0}^{m}N(r, 1_{0}\oslash f_{i})$ and the ramification term $N(r, C_{0}(f_{0}, \cdots, f_{m}))$, implying that there is no natural tropical truncated version of the second main theorem for shift operators.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
