非阿基米德亚纯函数的Ahlfors Islands定理

Non-Archimedean second main theorem sharing small functions

In this paper, we establish a new second main theorem for meromorphic functions on a non-Archimedean field and small functions with counting functions truncated to level $1.$ As an application, we show that two meromorphic functions on a non-Archimedean field must coincide to each other if they share $q\, (q\geq 5)$ distinct small functions ignoring multiplicities. In particular, if two non-Archimedean meromorphic functions share $5$ small functions ignoring multiplicities, they must be identical. Thus, our work improves the results in \cite{EY}.

非阿基米德亚纯映射的截断第二主定理

Truncated second main theorem for non-Archimedean meromorphic maps

本文研究了特征 $p\ge 0$ 完备非阿基米德代数闭域上的亚纯映射，证明了 $\mathbb F^m$ 到射影子簇 $V$ 且与 $N-$次一般位置超曲面族相交的截断第二主定理。

Lectures on Non-Archimedean Function Theory

Lecture 1 discusses non-Archimedean analogs of classical complex function theory based on the Schnirelman integral. Lecture 2 discusses valuation (Newton) polygons and their consequences and presents a non-Archimedean analog of the Poisson-Jensen formula. Lecture 3 introduces non-Archimedean value distribution theory. Lecture 4 presents an introduction to Benedetto's non-Archimedean analogs of the Ahlfors Island theorems.

关于亚纯函数的ABC定理

The ABC Theorem for Meromorphic Functions

使用一个“高度到根”的身份，我们定义了阿基米德的贡献的根，$r_\arch$，我们给了一个新的证明的ABC定理的领域的亚纯函数。证明的第一步是完全形式化的，并得出高度由根式$h\leq r$限定，其中$r=r_\na+r_\arch$是用阿基米德贡献完成的根式。第二步本质上是解析的，并使用对数导数引理推导出$r_\arch$的界。

Local Zeta Functions, pseudodifferential operators, and Sobolev-type spaces over non-Archimedean Local Fields

In this article we introduce a new type of local zeta functions and study some connections with pseudodifferential operators in the framework of non-Archimedean fields. The new local zeta functions are defined by integrating complex powers of norms of polynomials multiplied by infinitely pseudo-differentiable functions. In characteristic zero, the new local zeta functions admit meromorphic continuations to the whole complex plane, but they are not rational functions. The real parts of the possible poles have a description similar to the poles of Archimedean zeta functions. But they can be irra…

A non-Archimedean analogue of Campana's notion of specialness

Let $K$ be an algebraically closed, complete, non-Archimedean valued field of characteristic zero, and let $\mathscr{X}$ be a $K$-analytic space (in the sense of Huber). In this work, we pursue a non-Archimedean characterization of Campana's notion of specialness. We say $\mathscr{X}$ is $K$-analytically special if there exists a connected, finite type algebraic group $G/K$, a dense open subset $\mathscr{U}\subset G^{\text{an}}$ with $\text{codim}(G^{\text{an}}\setminus \mathscr{U}) \geq 2$, and an analytic morphism $\mathscr{U} \to \mathscr{X}$ which is Zariski dense. With this definition, we…