FOR 570: Algebraic Cycles and L-functions

FOR 570：代数圈和 L 函数

• 批准号: 5471524
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2005
• 资助国家: 德国
• 起止时间: 2004-12-31 至 2011-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5471524?language=en
• 关键词: 570; Algebraic; Cycles; functions

The research project belongs to the intersection of number theory and algebraic geometry inside mathematics. Basic for number theory is the problem to solve algebraic equations and to make as far as possible quantitative and qualitative statements about these solutions. For this purpose, it has become useful to encode the number of solutions (over finite fields for every prime number p) in the so-called L-function. Many deep statements can be or should be read of from the properties of the L-function. We mention the Riemann conjecture and the Birch-Swinnerton-Dyer conjecture, two of the seven millennium price problems of mathematics.

本课题属于数学中数论与代数几何的交叉学科。数论的基础是解决代数方程的问题，并尽可能地对这些解进行定量和定性的陈述。为了这个目的，它已成为有用的编码的解决方案的数量（在有限域上的每一个素数p）在所谓的L函数。许多深度语句可以或者应该从L函数的属性中读取。我们提到了Riemann猜想和Birch-Swinnerton-Dyer猜想，这是七个千年数学价格问题中的两个。