Mathematical Sciences: Diophantine Equations, Diophantine Approximation and Geometry

数学科学：丢番图方程、丢番图近似和几何

• 批准号: 8701396
• 负责人: Jeffrey Vaaler
• 金额: $ 3.82万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-06-15 至 1990-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8701396&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Diophantine; Equations; Approximation

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.

这项研究将研究丢番图近似和解析数论中的各种问题。 主题之一是研究某些丢番图方程的解，已知这些方程具有非平凡解，因此必须具有小高度的解。 该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有关整数和实数有理近似的问题。 他将在当前的研究中推进这些调查。 在许多问题中，重要的是要知道可以获得某些方程的解，并且可以精确测量解的大小。 这将是当前研究的一个主要主题，尽管在这个基础广泛的研究中还有许多其他主题。 该计划将引起人们极大的兴趣。