FOR 570: Algebraic Cycles and L-functions

本课题属于数论与代数几何在数学中的交叉领域。数论的基本问题是求解代数方程，并尽可能地对这些解作出定量和定性的表述。为此，在所谓的l函数中编码解的数量（在有限域上对每个素数p）变得很有用。可以或应该从l函数的性质中读出许多深奥的语句。我们提到了黎曼猜想和伯奇-斯温纳顿-戴尔猜想，这是七个千年数学难题中的两个。

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.