Reciprocity via Reciprocants

Authors: Matthew Baker

10 pages. v2: Rewrote Appendix B, fixed miscellaneous typos
License: CC BY 4.0

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.

Submitted to arXiv on 05 Sep. 2023

Explore the paper tree

Click on the tree nodes to be redirected to a given paper and access their summaries and virtual assistant

Also access our AI generated Summaries, or ask questions about this paper to our AI assistant.

Look for similar papers (in beta version)

By clicking on the button above, our algorithm will scan all papers in our database to find the closest based on the contents of the full papers and not just on metadata. Please note that it only works for papers that we have generated summaries for and you can rerun it from time to time to get a more accurate result while our database grows.