Generalized ABC theorems for non-Archimedean entire functions of several variables in arbitrary characteristic

The ABC Theorem for Meromorphic Functions

Using a `height-to-radical' identity, we define the archimedean contribution to the radical, $r_\arch$, and we give a new proof of the abc theorem for the field of meromorphic functions. The first step of the proof is completely formal and yields that the height is bounded by the radical, $h\leq r$, where $r=r_\na+r_\arch$ is the radical completed with the archimedean contribution. The second step is analytic in nature and uses the lemma on the logarithmic derivative to derive a bound for $r_\arch$.

整函数的差分“abc”定理与Nevanlinna第二主定理截断版本的差分类似

Difference "abc" theorem for entire functions and Difference analogue of truncated version of Nevanlinna second main theorem

本文研究了阶小于1的整函数的差分$abc$定理及Nevanlinna第二主定理截断版本的差分类似，揭示了次正规亚纯函数在复平面上具有长长度点的数量限制，并应用于差分Fermat泛函方程的整解。

Non-archimedean entire curves in closed subvarieties of semi-abelian varieties

We prove a non-archimedean analogue of the fact that a closed subvariety of a semi-abelian variety is hyperbolic modulo its special locus, and thereby generalize a result of Cherry.

控制椭圆曲线的射影簇中的非阿基米德整曲线

Non-Archimedean entire curves in projective varieties dominating an elliptic curve

本文针对允许支配态射到椭圆曲线的无群射影曲面，证明其 K-解析 Brody 双曲性，从而建立不规则度为一情形的非阿基米德 Green–Griffiths–Lang 猜想。

Motohashi's fourth moment identity for non-archimedean test functions and applications

Motohashi established an explicit identity between the fourth moment of the Riemann zeta function weighted by some test function and a spectral cubic moment of automorphic L-functions. By an entirely different method, we prove a generalization of this formula to a fourth moment of Dirichlet L-functions modulo q weighted by a non-archimedean test function. This establishes a new reciprocity formula. As an application, we obtain sharp upper bounds for the fourth moment twisted by the square of a Dirichlet polynomial of length q^{1/4}. An auxiliary result of independent interest is a sharp upper …

函数域上阿贝尔簇的GCD与ABC不等式

GCD and ABC inequalities for abelian varieties over function fields

该研究证明了特征0函数域上阿贝尔簇有理点的GCD不等式与几何abc猜想的特殊情形，采用三步证明模式，借助Xie-Yuan高度等工具解决了Buium的相关猜想。