Effective methods in number theory

数论中的有效方法

• 批准号: RGPIN-2019-04223
• 负责人: Stewart, Cameron
• 金额: $ 2.33万
• 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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=764419
• 关键词: Effective; methods; number; theory

I 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 profound 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.

我计划研究数论中几个悬而未决的问题，涉及素数的分布和整数或有理数方程的解。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abc猜想，它是数学中最深刻的发现之一。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。