Topics in Number Theory

数论专题

• 批准号: 2100933
• 负责人: Kannan Soundararajan
• 金额: $ 62.5万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2100933&HistoricalAwards=false
• 关键词: Topics; Number; Theory

This award is concerned with problems in number theory, specifically the theory of L-functions. One central theme in number theory is to understand the properties and distribution of prime numbers. Often such problems are understood by packaging the relevant information into analytic objects known as L-functions. The study of these L-functions is a classical topic in number theory beginning with the work of Riemann and Dirichlet in the nineteenth century, but yet continues to be a central focus of modern mathematics, with problems like the Riemann Hypothesis and the Birch & Swinnerton-Dyer conjectures lying at the heart of the subject. Progress in this area has sometimes found applications in cryptography and theoretical computer science. The investigator will continue his work on topics at the interface of analysis, number theory, and combinatorics. In particular he will continue research in multiplicative number theory (for example in the distribution of random multiplicative functions, averages of Weyl sums, and averages of singular series), and in understanding the moments and value distribution of central values of L-functions. The grant will also be used to help train graduate students in the area.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该奖项涉及数字理论中的问题，特别是L功能理论。 数字理论的一个中心主题是了解质数的属性和分布。 通常，通过将相关信息包装到称为L功能的分析对象中，可以理解此类问题。 对这些L功能的研究是数字理论的一个古典主题，从19世纪Riemann和Dirichlet的工作开始，但仍是现代数学的核心重点，诸如Riemann假设以及Birch＆Swinnerton-Dyer猜想之类的问题。 该领域的进展有时在密码学和理论计算机科学中发现了应用。研究人员将继续在分析，数字理论和组合学界面上的主题上工作。 特别是他将继续研究乘法数理论（例如，在随机乘法函数的分布中，Weyl总和的平均值和单数序列的平均值），以及了解L函数中心值的力矩和价值分布。 该赠款还将用于帮助该地区的研究生培训研究生。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子和更广泛影响的评论标准来评估值得支持的。

项目成果

A model problem for multiplicative chaos in number theory

数论中乘性混沌的模型问题

• DOI: 10.4171/lem/1031
• 发表时间: 2022
• 期刊: L’Enseignement Mathématique
• 作者: Soundararajan, Kannan;Zaman, Asif
• 通讯作者: Zaman, Asif