Mathematical Sciences: Arithmetic Capacity Theory

这项研究的目的是继续主要的 容量算术应用研究 理论 此前，他提出了一种能力理论， 整体域上代数曲线上的椭圆集， 代数点的存在性和有限性准则， 幂级数的合理性准则 拟议研究 将寻求定量地提高已知的应用程序，追求 与其他领域的联系，并搜索概括， 更高的维度

The purpose of this research is to continue the principal investigator's study of arithmetic applications of capacity theory. Previously he has developed a theory of capacity for adelic sets on algebraic curves over global fields, yielding existence and finiteness criteria for algebraic points and rationality criteria for power series. The proposed research will seek to quantitatively sharpen known applications, pursue connections with other fields, and search for generalizations to higher dimensions.