The sextic period polynomial

D. H. Lehmer and Emma Lehmer

Vol. 111 (1984), No. 2, 341–355

DOI: 10.2140/pjm.1984.111.341

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

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