Mathematical Sciences: Nevanlinna Error Terms and p-Adic Analytic Curves

[505041] Cherry提出的研究是数论和几个复杂变量的接口。申请人想了解奈万林纳理论和丢番图几何之间的关系。特别是，他将研究奈万林纳理论中的误差项和全纯曲线的p进类似项。最近，在复杂几何和数论的某些领域之间的形式化类比已经被观察到。这是出乎意料的，因为这两个领域传统上是不相关的数学领域：数论处理整数方程，而复杂几何处理非离散对象。

9505041 Cherry The proposed research lies in the interface of number theory and several complex variables. The proposer wants to understand the relationship between Nevanlinna theory and diophantine geometry. In particular, he will study error terms in Nevanlinna theory and p-adic analogues of holomorphic curves. Recently, formal analogies between certain areas of complex geometry and number theory have been observed. This is unexpected in that these two areas are traditionally unrelated areas of mathematics: number theory deals with integer equations whereas complex geometry deals with non-discrete objects.