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arXiv · 1512.06480

Characterizations of quadratic, cubic, and quartic residue matrices

David S. Dummit·Evan P. Dummit·Hershy Kisilevsky
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Abstract

We construct a collection of matrices defined by quadratic residue symbols, termed "quadratic residue matrices", associated to the splitting behavior of prime ideals in a composite of quadratic extensions of $\mathbb{Q}$, and prove a simple criterion characterizing such matrices. We also study the analogous classes of matrices constructed from the cubic and quartic residue symbols for a set of prime ideals of $\mathbb{Q}(\sqrt{-3})$ and $\mathbb{Q}(i)$, respectively.

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David S. Dummit, Evan P. Dummit, Hershy Kisilevsky. 2015-12-21. Characterizations of quadratic, cubic, and quartic residue matrices. https://arxiv.org/abs/1512.06480

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