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Characterizations of the $d$th-power residue matrices over finite fields
| Content Provider | Semantic Scholar |
|---|---|
| Author | Dummit, Evan P. |
| Copyright Year | 2018 |
| Abstract | In a recent paper of the author with D. Dummit and H. Kisilevsky, we constructed 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 proved a simple criterion characterizing such matrices. We then analyzed 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. In this paper, the goal is to construct and study the finite-field analogues of these residue matrices, the "$d$th-power residue matrices", using the general $d$th-power residue symbol over a finite field. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1809.10225v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
