Characterizations of quadratic, cubic, and quartic residue matrices

摘要

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 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 Q(root-3) and Q(i), respectively. (C) 2016 Elsevier Inc. All rights reserved.