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Rational Reciprocity and Algebraic Number Fields Dr. Mark Budden, Armstrong Atlantic State University Mathematics Department


Abstract

Beginning with the initial investigations into quadratic reciprocity by Euler and Legendre, reciprocity laws served as a major driving-force behind the development of algebraic number theory until the 1930's. Today, students encounter the Law of Quadratic Reciprocity in elementary courses in number theory, but the vast number of generalizations of this law are rarely mentioned. In this talk, we will investigate a class of such generalizations, known as rational reciprocity laws, and discuss their relationship with primitive elements of algebraic number fields.
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