Periods and Special Values of L-functions

L 函数的周期和特殊值

• 批准号: 0200605
• 负责人: Fernando Rodriguez-Villegas
• 金额: $ 21.06万
• 依托单位: University of Texas at Austin
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-06-15 至 2008-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0200605&HistoricalAwards=false
• 关键词: Periods; Special; Values; functions

The PI and his collaborators, will continue their investigation of therelations between periods and special values ofL-functions. Specifically, those pertaining to the conjecture of Blochand Beilinson for elliptic curves and those implied by Borel's theoremfor a number field and their connection to the Mahler measure ofLaurent polynomials and the geometry of hyperbolic 3-manifolds.The PI's research area is in Number Theory, a very old subject withconnections to every other conceivable area of Mathematics as well asPhysics. It is remarkable how the type of questions one would like toanswer in Number Theory, for example, can we write the number 1 as thesum of the cubes of two rational numbers?, which at the time of Fermat(1600's) say, most likely had no direct implications to everyday life,have evolved into highly relevant issues today. In our currenttechnology age, Number Theory is behind much of the safety of commonactivities like, for example, shopping on the internet. The PI'sspecific research concerns L-functions, certain analytic objects oneassociates to questions like the one above, which are central tomodern Number Theory and from which one expects to, and often does,retrieve answers.

PI 和他的合作者将继续研究 L 函数的周期和特殊值之间的关系。具体来说，涉及 Blochand Beilinson 对椭圆曲线的猜想，以及 Borel 数域定理所暗示的那些，以及它们与洛朗多项式的马勒测度和双曲 3 流形几何的联系。 PI 的研究领域是数论，这是一个非常古老的学科，与数学和物理学的所有其他可以想象的领域都有联系。值得注意的是，人们在数论中想要回答的问题类型，例如，我们能否将数字 1 写成两个有理数的立方之和？，在费马（1600 年代）时代，这很可能对日常生活没有直接影响，但今天却演变成了高度相关的问题。在当今的技术时代，数论是许多常见活动（例如网上购物）安全性的基础。 PI 的具体研究涉及 L 函数，即与上述问题相关的某些分析对象，这些对象是现代数论的核心，人们期望并且经常从中找到答案。