Conference: Comparative Prime Number Theory Symposium

研讨会比较素数理论研讨会是第一次主要关注这一主题的科学活动，将于2024年6月17日至21日在温哥华大学温哥华校区举行。研究素数的分布是数论研究的首要和中心课题之一。1853年，契比雪夫观察到，以四加三的倍数形式出现的素数似乎比四加一的倍数多。这种现象现在被称为契比雪夫偏差，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子领域，这一领域的研究重点是考察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，这个领域见证了显著的发展和活动，特别是在1994年鲁宾斯坦和萨纳克发表了关于契比雪夫偏见的有影响力的文章之后。这个奖项的主要目标是提供参与者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。研讨会将汇集许多具有比较素数理论专业知识和兴趣的领先和职业早期研究人员，介绍和讨论该领域当前研究的各个方面，特别强调与数论中计数函数的分布和L函数的零点有关的结果，定量线性独立的后果，Merten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表的调查《比较素数理论的注释书目》，该调查旨在记录比较素数理论主题中的每一篇出版物，以及结果摘要，并提出一个统一的符号和术语体系，用于指代作为主要研究对象的量和假设。研讨会的另一个重要成果将是编制和公布问题清单，希望刺激未来的研究，并为年轻研究人员提供潜在的项目。有关会议的信息可在网站上找到：https://sites.google.com/view/crgl-functions/comparative-prime-number-theory-symposiumThis奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.