Zeta Functions and L-Functions Over Finite Fields

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9622895 Wan This grant supports the work of Professor D. Wan to work in arithmetic geometry specifically problems in the arithmetic of function fields. He intends to study the L-function attached to a continuos representations of the arithmetical fundamental group of an affine algebraic variety defined over a finite field of characteristic p. He intends to study rationality, possible meromorphic continuations, entireness and the Riemann hypothesis for these L-functions. This project falls into the general area of arithmetic 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.