Mathematical Sciences: Special Values of L-functions

Flach 9624824该奖项为算术代数几何的一个项目提供资金。该项目的中心是关于数域上的L-函数的特殊值。更具体地说，研究者将致力于玉川数猜想的伴随模形式，并对伽罗瓦模理论不变量的研究，其定义的动机是对特殊值的L-函数的命题。 这个项目福尔斯属于算术代数的一般领域 几何-一门融合了两个最古老的数学领域的学科：数论和几何。 事实证明，这种结合非常富有成效--最近解决了几代人都无法解决的问题。在它的许多后果是新的纠错码。 这种代码对于现代计算机（硬盘）和光盘都是必不可少的。

Flach 9624824 This award provides funding for a project in Arithmetic Algebraic Geometry. The project centers around the conjectures about special values of L-functions attached to varieties over number fields. More specifically, the investigator will work on the Tamagawa number conjecture for the adjoint of a modular form, and on the study of Galois module theoretic invariants whose definition is motivated by the conjectures on special values of L-functions. This project falls into the general area of Arithmetic Algebraic Geometry -a subject that blends two of the oldest areas of mathematics: Number Theory and Geometry. This combination has proved extraordinarily fruitful - having recently solved problems that withstood generations. Among its many consequences are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks.