The most natural extensions to the law of quadratic reciprocity are the rational reciprocity laws, described using the rational residue symbol. In this article, we provide a reciprocity law from which many of the known rational reciprocity laws may be recovered by picking appropriate primitive elements for subfields of . As an example, a new generalization of Burde’s law is provided.
"Rational residuacity of primes." Involve 3 (3) 249 - 257, 2010. https://doi.org/10.2140/involve.2010.3.249