Student Number Theory Seminar

David Urbanik, University of Waterloo

"What is a reciprocity law?"

There are numerous theorems in algebraic number theory which are "reciprocity laws". The simplest of these is quadratic reciprocity, for which there are many elementary proofs. For higher powers, there are many similar-looking statements, but whose proofs become progressively harder. We survey a number of reciprocity laws, give proofs of some simple ones, and try to show that they are all related.

MC 5403