Reciprocity via Reciprocants
Number Theory
2023-09-12 v2
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.
Cite
@article{arxiv.2309.02512,
title = {Reciprocity via Reciprocants},
author = {Matthew Baker},
journal= {arXiv preprint arXiv:2309.02512},
year = {2023}
}
Comments
10 pages. v2: Rewrote Appendix B, fixed miscellaneous typos