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。该项目围绕着关于L的特殊值的猜想--赋于数域上的变种的函数。更具体地说，研究者将致力于模形式的伴随的玉马川数猜想，以及伽罗华模理论不变量的研究，其定义是由关于L-函数的特殊值的猜想引发的。这个项目属于算术代数几何的一般领域--一门融合了数论和几何这两个最古老的数学领域的学科。事实证明，这种结合非常有成效--最近解决了几代人经受住的问题。在其众多后果中，有一种是新的纠错码。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.