Reciprocity via Reciprocants
arXiv:2309.02512
Abstract
The determinant of a skew-symmetric matrix has a canonical square root given by the Pfaffian. Similarly, the resultant of two reciprocal polynomials of even degree has a canonical square root given by their reciprocant. Computing the reciprocant of two cyclotomic polynomials yields a short and elegant proof of the Law of Quadratic Reciprocity.
10 pages. v2: Rewrote Appendix B, fixed miscellaneous typos