Mathematical Sciences: Arithmetic Capacity Theory

本研究的目的是继续主要研究者对容量理论的算术应用的研究。在此之前，他发展了整体域上代数曲线上幂集的容量理论，给出了代数点的存在性和有限性准则以及幂级数的合理性准则。拟议的研究将寻求定量地强化已知应用，追求与其他领域的联系，并寻找更高维度的概括。

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.