Reciprocity via Reciprocants

Matthew Baker

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arXiv · 2309.02512

Reciprocity via Reciprocants

Matthew Baker

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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.

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Matthew Baker. 2023-09-05. Reciprocity via Reciprocants. https://arxiv.org/abs/2309.02512

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