Families of irreducible polynomials of Gaussian periods and matrices of cyclotomic numbers

Given an odd prime p we show a way to construct large families of polynomials Pq(x) Q[x], q C, where C is a set of primes of the form q 1 mod p and Pq(x) is the irreducible polynomial of the Gaussian periods of degree p in Q(q). Examples of these families when p = 7 are worked in detail. We also show, given an integer n 2 and a prime q 1 mod 2n, how to represent by matrices the Gaussian periods 0, . . . , n-1 of degree n in Q(q), and how to calculate in a simple way, with the help of a computer, irreducible polynomials for elements of Q(0).

• Type: Journal
• Year: 2000
• Where: MOC
• Authors: F. Thaine
• Keywords: Irreducible Polynomials, MOC 2000, Odd Prime, Polynomials