On Exponential Sums and Additive Diophantine Equations

关于指数和和可加性丢番图方程

• 批准号: 9303505
• 负责人: Trevor Wooley
• 金额: $ 5.55万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-06-01 至 1996-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9303505&HistoricalAwards=false
• 关键词: Exponential; Sums; Additive; Diophantine; Equations

This proposal is concerned with bounds for mean values in additive number theory, and the local solubility of simultaneous additive equations. The principal investigator intends to improve estimates in Vinogradov's mean value theorem by incorporating the ideas behind the new refinements in the corresponding work in Waring's problem. These improvements will have consequences beyond additive number theory. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.

该提议涉及加法数论中平均值的界限以及联立加法方程的局部可溶性。 首席研究员打算通过将新改进背后的思想纳入沃林问题的相应工作中来改进维诺格拉多夫中值定理的估计。 这些改进将产生超出加法数论的影响。 这是数论领域的研究。 数论从整数和诸如一个整数能否被另一个整数整除之类的问题开始。 它是最古老的数学领域之一，最初纯粹出于美学原因而追求它。 然而，在过去的半个世纪中，它已成为开发计算机科学新算法和电子学新纠错码的重要工具。