Professor Jochnowitz proposes to investigate p-adic properties of modular forms of half integral weight and the Shimura correspondence between forms of half integral weight and integral weight. She hopes to apply the results of these investigations to elliptic curves and class numbers of quadratic fields. 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.
