Dynamical Approaches to Number Theory and Additive Combinatorics

数论和加法组合学的动态方法

• 批准号: EP/Y014030/1
• 负责人: Joel Moreira
• 金额: $ 161.86万
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FY014030%2F1
• 关键词: Dynamical; Approaches; Number; Theory; Additive

In the last few decades, dynamical approaches to problems arising in Ramsey theory, Additive Combinatorics and Number theory have been rather successful. Some very recent techniques, pioneered by the PI and other researchers, widen the range of applications of these ideas to some problems previously out of reach. This proposal seeks to build upon these novel ideas in order to gain new insight into some fundamental problems in those areas.The range of problems we propose to investigate include questions about partition regularity of polynomial configurations in the natural numbers; questions about the statistical behavior of multiplicative functions, and the question of which infinite configurations are present in every set of positive density.Despite looking unrelated, there are deep connections between all these problems, often formulated in the language of ergodic theory or dynamical systems.

在过去的几十年里，拉姆齐理论、加法组合学和数论中出现的问题的动态方法已经相当成功。由 PI 和其他研究人员首创的一些最新技术扩大了这些想法的应用范围，解决了一些以前无法解决的问题。该提案旨在以这些新颖的想法为基础，以便对这些领域的一些基本问题获得新的见解。我们建议研究的问题范围包括有关自然数中多项式配置的划分正则性的问题；关于乘法函数的统计行为的问题，以及每组正密度中存在无限配置的问题。尽管看起来无关，但所有这些问题之间存在着深刻的联系，通常用遍历理论或动力系统的语言来表述。