Conference: Comparative Prime Number Theory Symposium

比较素数理论研讨会将于2024年6月17日至21日在UBC温哥华校区举行，这是第一个主要关注这一主题的科学活动。数论研究的首要和中心课题之一是研究素数的分布。在1853年，切比雪夫观察到似乎有更多的质数是4加3的倍数，而不是4加1的倍数。这种现象现在被称为切比雪夫偏差，它的研究导致了数论的一个新分支，比较素数理论。作为解析数论的一个分支，该领域的研究主要集中在质数函数和其他算术函数之间的比较。这一领域在过去三十年中有了显著的发展和活跃，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，使他们有机会讨论新的想法，推进研究项目，并与已有的研究人员进行互动。本次研讨会将汇集许多在比较素数理论方面具有专业知识和兴趣的领先和早期职业研究人员，介绍和讨论该领域当前研究的各个方面，特别强调数论中计数函数的分布和l函数的零点，定量线性无关的后果，默滕斯和的振荡，以及符号变化的频率。通过这次研讨会，我们将宣传马丁等人最近发布的调查“比较素数理论注释书目”，该调查旨在记录比较素数理论主题内的每一篇出版物，连同结果摘要，并提出一个统一的符号和术语系统，用于参考作为主要研究对象的数量和假设。讨论会的另一项重要成果将是编制和公布一份问题清单，以期促进未来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网站上找到：https://sites.google.com/view/crgl-functions/comparative-prime-number-theory-symposiumThis该奖项反映了美国国家科学基金会的法定使命，并通过基金会的智力价值和更广泛的影响审查标准进行评估，认为值得支持。

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.