Effective methods in number theory

数论中的有效方法

• 批准号: 3528-2013
• 负责人: Stewart, Cameron
• 金额: $ 2.77万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=665956
• 关键词: Effective; methods; number; theory

We plan to investigate several open questions in number theory concerning the distribution of prime numbers and the solution of equations in integers or rational numbers. These topics have a distinguished history which can be traced back to the ancient Greeks and yet they are relevant today in the construction of error correcting codes and for cryptographic purposes. We shall focus on the abc conjecture which is one of the most important conjectures in mathematics. It provides a link between the additive and multiplicative structure of the integers and many of the most interesting questions in number theory depend on this link.**

我们计划研究数论中关于素数分布和整数或有理数方程解的几个开放性问题。这些主题有着悠久的历史，可以追溯到古希腊，但它们在今天的纠错码和密码学目的的建设中是相关的。我们将集中讨论数学中最重要的猜想之一abc猜想。它提供了整数的加法和乘法结构之间的联系，数论中许多最有趣的问题都依赖于这个联系。