Mathematical Sciences: RUI: Derivatives of L-Series for Elliptic Curves over Function Fields

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This research is concerned with the arithmetic of function fields. The principal investigator will study Heegner points on modular curves with a view to proving an analog of the theorem of Gross and Zagier. 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.