2018/09/26 by Dummit, Evan P.
#05B20 #12E20 #FOS: Mathematics #Number Theory (math.NT) #Primary 11A15 #Secondary 11T06
paper · doi:10.48550/arxiv.1809.10225
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 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 ℚ(√(-3)) and ℚ(i), respectively. In this paper, the goal is to construct and study the finite-field analogues of these residue matrices, the "dth-power residue matrices", using the general dth-power residue symbol over a finite field.