Vol. 111, No. 2, 1984

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The sextic period polynomial

D. H. Lehmer and Emma Lehmer

Vol. 111 (1984), No. 2, 341–355
Abstract

The coefficients of the polynomial whose roots are the six periods of the p-th roots of unity are given for every prime p = 6f + 1 in terms of L and M in the quadratic partition

4p = L2 +27M 2.

An explicit formula for the discriminant of this polynomial is also given. A complete analysis of the prime factors of the integers represented by the period polynomial and its corresponding form is given.

Mathematical Subject Classification 2000
Primary: 11L03
Secondary: 11T06
Milestones
Received: 16 August 1982
Published: 1 April 1984
Authors
D. H. Lehmer
Emma Lehmer