Mathematical Sciences: P-Adic Constructions on Elliptic Curves

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Rubin works in the area of the arithemetic of elliptic curves and the Birch and Swinnerton-Dyer conjecture. The major focus of the proposal is to generalize to modular elliptic curves a new method discovered by Rubin which uses special values of p-adic L- functions to construct rational points of infinite order on rank-1 elliptic curves with complex multiplication. This is research in the field of number theory. Number theory starts with the whole numbers and questions such as the divisibility of one whole number by another. It is among the oldest fields of mathematics and it was originally pursued for purely aesthetic reasons. However, within the last half century, it has become an essential tool in developing new algorithms for computer science and new error correcting codes for electronics.