# Reciprocity via Reciprocants

**Authors:** Matthew Baker  
**arXiv:** [2309.02512](https://arxiv.org/abs/2309.02512)  
**Date:** 2023-09-05  
**Summary page:** https://www.summarizepaper.com/en/paper/2309.02512v2/

## 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.