Diophantine Approximation of Algebraic Points

9970393本项目研究全纯函数的丢番图逼近和值分布理论。 工作C。首席研究员奥斯古德和其他人已经证明，这两个领域实际上是由一个正式的类比联系在一起的。 这一观察导致了新的证明，现有定理的较短证明，以及新定理的证明。 这个项目将扩展类比，主要但不完全是在丢番图逼近领域。数论是研究整数和有理数的性质。 其中很大一部分用于研究多项式方程组的整数和有理数解。 这项研究的一个特别的方法是看这样的解决方案所满足的不平等。 这种方法，称为丢番图近似，通常用于证明给定的多项式方程组很少有整数或有理解。

9970393This project deals with diophantine approximation and value distribution theory of holomorphic functions. Work by C. Osgood, the Principal Investigator, and others has shown that these two fields are in fact connected by a formal analogy. This observation has led to new conjectures, shorter proofs of existing theorems, and proofs of new theorems. This project will extend the analogy, working primarily but not entirely in the field of diophantine approximation.Number theory is the study of the properties of whole numbers and ]rational numbers. A large part of this is devoted to studying whole-number and rational-number solutions to systems of polynomial equations. One particular approach to this study has been to look at inequalities satisfied by such solutions. This approach, called diophantine approximation, is often useful for proving that there are few integer or rational solutions to a given set of polynomial equations.