Conference: Comparative Prime Number Theory Symposium

会议：比较素数论研讨会

• 批准号: 2411537
• 负责人: Wanlin Li
• 金额: $ 1万
• 依托单位: Washington University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-05-01 至 2025-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2411537&HistoricalAwards=false
• 关键词: Conference; Comparative; Prime; Number; Theory

The workshop Comparative Prime Number Theory Symposium, which is the first scientific event to focus predominantly on this subject, will take place on the UBC--Vancouver campus from June 17--21, 2024. One of the first and central topics in the research of number theory is to study the distribution of prime numbers. In 1853, Chebyshev observed that there seems to be more primes taking the form of a multiple of four plus three than a multiple of four plus one. This phenomenon is now referred to as Chebyshev's bias and its study led to a new branch of number theory, comparative prime number theory. As a subfield of analytic number theory, research in this area focuses on examining how prime counting functions and other arithmetic functions compare to one another. This field has witnessed significant growth and activity in the last three decades, especially after the publication of the influential article on Chebyshev's bias by Rubinstein and Sarnak in 1994. The primary goal of this award will be to provide participant support and fund US-based early career researchers to attend this unique event, giving them the opportunity to discuss new ideas, advance research projects, and interact with established researchers.The symposium will bring together many leading and early-career researchers with expertise and interest in comparative prime number theory to present and discuss various aspects of current research in the field, with special emphasis on results pertaining to the distribution of counting functions in number theory and zeros of L-functions, consequences of quantitative Linear Independence, oscillations of the Mertens sum, and the frequency of sign changes. Through this symposium, we will advertise the recently disseminated survey "An Annotated Bibliography for Comparative Prime Number Theory" by Martin et al which aims to record every publication within the topic of comparative prime number theory, together with a summary of results, and presenting a unified system of notation and terminology for referring to the quantities and hypotheses that are the main objects of study. Another important outcome of the symposium will be compiling and publicizing a problem list, with the hope of stimulating future research and providing young researchers with potential projects. Information about the conference can be found at the website: https://sites.google.com/view/crgl-functions/comparative-prime-number-theory-symposiumThis 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.

研讨会比较素数理论研讨会，这是第一个主要关注这一主题的科学活动，将于2024年6月17日至21日在UBC-温哥华校区举行。素数分布的研究是数论研究的首要和中心课题之一。在1853年，切比雪夫观察到，似乎有更多的素数的形式是4 + 3的倍数，而不是4 + 1的倍数。这种现象现在被称为切比雪夫的偏见和它的研究导致了一个新的分支数论，比较素数理论。作为解析数论的一个分支，这一领域的研究重点是研究素数计数函数和其他算术函数之间的比较。在过去的三十年里，这一领域见证了显着的增长和活动，特别是在1994年鲁宾斯坦和萨尔纳克发表了关于切比雪夫偏见的有影响力的文章之后。 该奖项的主要目标将是为参与者提供支持，并资助美国的早期职业研究人员参加这一独特的活动，让他们有机会讨论新的想法，推进研究项目，并与知名研究人员互动。研讨会将汇集许多领先和早期-职业研究人员的专业知识和兴趣比较素数理论提出和讨论目前的研究领域的各个方面，特别强调结果有关的分布计数函数在数论和零点的L-功能，后果的定量线性独立性，振荡的Mertens和，和频率的符号变化。通过这次研讨会，我们将宣传最近传播的调查“比较素数理论的注释书目”马丁等人，其目的是记录比较素数理论主题内的每一篇出版物，以及结果摘要，并提出一个统一的符号和术语系统，用于引用作为主要研究对象的量和假设。研讨会的另一项重要成果是汇编和公布一份问题清单，以期促进今后的研究，并为年轻研究人员提供潜在的项目。有关会议的信息可以在以下网站上找到：https://sites.google.com/view/crgl-functions/comparative-prime-number-theory-symposiumThis奖项反映了NSF的法定使命，并被认为值得通过使用基金会的知识价值和更广泛的影响审查标准进行评估来支持。