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2000

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

13 years 3 months ago
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).
F. Thaine
Added 19 Dec 2010
Updated 19 Dec 2010
Type Journal
Year 2000
Where MOC
Authors F. Thaine
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