Mathematical Sciences: Special Values of L-functions

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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.