Graduate workshop on zeta functions, L-functions and their applications; Summer 2009, Orem, UT

zeta 函数、L 函数及其应用研究生研讨会；

• 批准号: 0910714
• 负责人: Roger Baker
• 金额: $ 1.8万
• 依托单位: Brigham Young University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-02-01 至 2010-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0910714&HistoricalAwards=false
• 关键词: Graduate; workshop; zeta; functions; their

ABSTRACT Principal Investigator: Baker, Roger C.Proposal Number: DMS - 0910714 Institution: Brigham Young University Title: Graduate workshop on zeta functions, L-functions and their applicationsThe Graduate Workshop on Zeta Functions, L-functions and Their Applications will be held at Utah Valley University on June 1-4, 2009. NSF funds will be used for travel and lodging for 20 participants including plenary speakers and students. The Riemann zeta function has gained enormous importance in the eyes of number theorists since its properties (expressed in terms easily understandable to a modern undergraduate studying complex analysis) were developed by Riemann in a renowned lecture in Berlin in 1859. Since then, the function has been used to prove the fundamental theorem on the distribution of prime numbers, and many other important results in number theory. The Dirichlet L-functions, and other zeta functions and L-functions invented since that time by Dedekind, Hecke, Artin and others, have vastly extended the range of application of Riemann's ideas, yet many conundrums remain about their properties. The workshop will have three sets of lectures by experts in the field: Brian Conrey, Ram Murty and Steve Gonek. Also, there will be about 16 talks by junior mathematicians and senior researchers. The three principal lecturers will discuss the ideas of zeta functions and L-functions beginning with the Riemann zeta function and Dirichlet L-functions, Dedekind zeta functions, and L-functions of number fields. They will also introduce automorphic L-functions, Artin L-functions and L-functions of varieties. Introductory concepts and results will be given in some detail. Modern topics such as the Birch-Swinnerton-Dyer conjecture and the random matrix approach to results and conjectures concerning zeta functions and L-functions will also be outlined. It is highly desirable to give graduate students working in number theory a broad picture of the state of the art in this subject area. The major component of the conference is the involvement of graduate students. This includes a certain number of talks reserved for graduate students who have results in the area to report. In addition, the conference will provide an opportunity for graduate students to interact with established researchers. This interaction will be promoted by scheduling breaks in which the participants will be encouraged to break up into groups to discuss research ideas. At the end of the workshop there will be a round table discussion on open problems and directions for future research. This will help stimulate the interest of graduate students and new PhDs.

摘要 首席研究员：Baker, Roger C. 提案编号：DMS - 0910714 机构：杨百翰大学 标题：zeta 函数、L 函数及其应用研究生研讨会 Zeta 函数、L 函数及其应用研究生研讨会将于 2009 年 6 月 1 日至 4 日在犹他谷大学举行。 NSF 资金将用于 20 名参与者（包括全体会议）的旅行和住宿 演讲者和学生。 黎曼 zeta 函数在数论学家眼中具有巨大的重要性，因为它的性质（以学习复分析的现代本科生容易理解的术语表达）是由黎曼于 1859 年在柏林的一次著名演讲中提出的。从那时起，该函数就被用来证明素数分布的基本定理以及数论中的许多其他重要结果。狄利克雷 L 函数以及 Dedekind、Hecke、Artin 等人自那时起发明的其他 zeta 函数和 L 函数极大地扩展了黎曼思想的应用范围，但有关其性质的许多难题仍然存在。 该研讨会将由该领域的专家进行三组讲座：Brian Conrey、Ram Murty 和 Steve Gonek。此外，初级数学家和高级研究人员还将进行约 16 场演讲。三位主讲人将从黎曼zeta函数和狄利克雷L函数、戴德金zeta函数和数域L函数开始讨论zeta函数和L函数的思想。他们还将引入自同构 L 函数、Artin L 函数和变种 L 函数。将详细给出介绍性概念和结果。还将概述现代主题，例如 Birch-Swinnerton-Dyer 猜想以及有关 zeta 函数和 L 函数的结果和猜想的随机矩阵方法。非常希望让研究数论的研究生对这个学科领域的最新技术有一个广泛的了解。会议的主要内容是研究生的参与。这包括为在该领域有成果报告的研究生保留一定数量的演讲。此外，会议将为研究生提供与知名研究人员互动的机会。这种互动将通过安排休息来促进，鼓励参与者分成小组讨论研究想法。研讨会结束时，将就开放问题和未来研究方向进行圆桌讨论。这将有助于激发研究生和新博士的兴趣。