Rational Reciprocity Laws
Emma T. Lehmer · American Mathematical Monthly · 1978
It is well known that the famous Legendre law of quadratic reciprocity, of which over 150 proofs are in print, has been generalized over the years to algebraic fields by a number of famous mathematicians from Gauss to Artin to the extent that it has become virtually unrecognizable. On the other hand, it seems to have escaped notice that in the past decade there were developed rational reciprocity laws for higher power residues which are more direct and easily recognizable generalizations of the Legendre law. These recent developments will be the subject of this report.