Analytic and Combinatorial Problems in Number Theory
数论中的分析和组合问题
基本信息
- 批准号:1702296
- 负责人:
- 金额:$ 10.65万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2017
- 资助国家:美国
- 起止时间:2017-08-01 至 2021-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Number theory is the study of integers. One central notion in number theory is that of prime numbers (i.e., numbers divisible only by themselves and one). These are the building blocks of the integers. While originally studied for purely aesthetic reasons, for several decades number theory and prime numbers have found practical applications in computer science (e.g., in coding theory) and cryptography. As such, prime numbers are ubiquitous in real life (e.g., in cryptosystems to encode messages sent over the Internet). The research in this project is directed at some problems in number theory using tools from analysis and combinatorics. This area, also known as arithmetic combinatorics, has seen tremendous growth in recent years due to its connection with other branches of mathematics as well as theoretical computer science.This project will explore configurations pertaining to dense subsets of the integers and the primes. Thanks to the insights of Szemeredi, Furstenberg, Gowers, Green and Tao, among others, many advances have been made, but there are still many questions to answer and interesting configurations to explore. Furthermore, recent breakthroughs on the twin prime conjecture due to Zhang, Maynard, and Tao give more insights on the primes and the PI intends to find patterns in almost twin primes. He will also study the function field model, in which one has more tools but where additional complications also arise. For example, the understanding of the distribution of high-degree polynomials in function fields is still incomplete due to the failure of Weyl differencing in low characteristic.
数论是研究整数的学科。数论中的一个中心概念是质数(即只能被自己和1整除的数)。这些是整数的组成部分。虽然最初纯粹是出于美学原因而研究,但几十年来,数论和素数在计算机科学(例如编码理论)和密码学中找到了实际应用。因此,质数在现实生活中无处不在(例如,在通过互联网发送的消息编码的密码系统中)。本课题利用分析学和组合学的工具研究数论中的一些问题。这个领域,也被称为算术组合学,近年来由于它与数学的其他分支以及理论计算机科学的联系而取得了巨大的增长。这个项目将探索关于整数和素数的密集子集的配置。由于Szemeredi, Furstenberg, Gowers, Green和Tao等人的见解,已经取得了许多进展,但仍有许多问题需要回答,还有许多有趣的配置需要探索。此外,由于Zhang、Maynard和Tao最近在孪生素数猜想上的突破,使人们对素数有了更多的了解,PI打算在几乎孪生素数中找到模式。他还将研究函数场模型,其中有更多的工具,但也会产生额外的复杂性。例如,由于低特征Weyl差分的失效,对函数场中高次多项式的分布的理解仍然不完整。
项目成果
期刊论文数量(5)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Multidimensional configurations in the primes with shifted prime steps
具有移动素数步长的素数中的多维构型
- DOI:10.1007/s10474-021-01143-9
- 发表时间:2021
- 期刊:
- 影响因子:0.9
- 作者:Le, A. N.;Lê, T. H.
- 通讯作者:Lê, T. H.
On theorems of Wirsing and Sanders
关于维尔辛和桑德斯定理
- DOI:10.4064/aa180125-20-9
- 发表时间:2019
- 期刊:
- 影响因子:0.7
- 作者:Ge, Zhenchao;Lê, Thái Hoàng
- 通讯作者:Lê, Thái Hoàng
LINEAR AND QUADRATIC UNIFORMITY OF THE MÖBIUS FUNCTION OVER
莫比乌斯函数的线性和二次均匀性
- DOI:10.1112/s0025579319000032
- 发表时间:2019
- 期刊:
- 影响因子:0.8
- 作者:Bienvenu, Pierre-Yves;Lê, Thái Hoàng
- 通讯作者:Lê, Thái Hoàng
Van der Corput sets with respect to compact groups
范德科普特集关于紧群
- DOI:10.1007/s00013-017-1136-y
- 发表时间:2018
- 期刊:
- 影响因子:0.6
- 作者:Kelly, Michael;Lê, Thái Hoàng
- 通讯作者:Lê, Thái Hoàng
A bilinear Bogolyubov theorem
双线性 Bogolyubov 定理
- DOI:10.1016/j.ejc.2018.11.003
- 发表时间:2019
- 期刊:
- 影响因子:1
- 作者:Bienvenu, Pierre-Yves;Lê, Thái Hoàng
- 通讯作者:Lê, Thái Hoàng
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Thai Hoang Le其他文献
Selective pressure of various levels of erythromycin on the development of antibiotic resistance
不同水平红霉素对产生抗生素抗性的选择压力
- DOI:
10.1016/j.envpol.2025.125757 - 发表时间:
2025-03-01 - 期刊:
- 影响因子:7.300
- 作者:
Tianren Wang;Xinzhu Yi;Thai Hoang Le;Vaishnavi Sivachidambaram;Zhi Zhou - 通讯作者:
Zhi Zhou
Fingerprint reference point detection for image retrieval based on symmetry and variation
- DOI:
10.1016/j.patcog.2012.02.017 - 发表时间:
2012-09-01 - 期刊:
- 影响因子:8
- 作者:
Thai Hoang Le;Hoang Thien Van - 通讯作者:
Hoang Thien Van
Thai Hoang Le的其他文献
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{{ truncateString('Thai Hoang Le', 18)}}的其他基金
Additive and Combinatorial Problems in Groups
群中的加法和组合问题
- 批准号:
2246921 - 财政年份:2023
- 资助金额:
$ 10.65万 - 项目类别:
Standard Grant
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