Mathematical Sciences: Diophantine Equations, Diophantine Approximation and Geometry

这项研究将研究丢番图逼近和解析数论中的各种问题。其中一个主要主题将是研究某些丢番图方程的解，这些方程已知有非平凡的解，因此肯定有小高度的解。这位首席研究员是数论领域的专家，他使用复杂的分析工具来回答关于整数和实数的有理逼近的问题。他将在目前的研究中推进这些调查。在许多问题中，了解某些方程的解是可能的，这一点很重要，因为人们对这些方程的解有多大有精确的测量。这将是当前研究的一个主要主题，尽管在这项基础广泛的研究中还有许多其他主题。这项计划将引起人们极大的兴趣。

This research will study various problems in diophantine approximations and analytic number theory. One of the main themes will be the study of solutions of certain diophantine equations which are known to have nontrivial solutions and therefore must have solutions of small height. This Principal Investigator is an expert in the area of number theory which uses sophisticated analytic tools to answer questions about the integers and the rational approximations of real numbers. He will carry forward these investigations in the current research. It is important in many problems to know that it is possible to obtain solutions to certain equations for which one has precise measures on how big the solutions are. This will be a major theme of the current research, although there are many others in this broadly based research. Much of great interest will result from this program.