Vol. 4, No. 4, 2011

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The family of ternary cyclotomic polynomials with one free prime

Yves Gallot, Pieter Moree and Robert Wilms

Vol. 4 (2011), No. 4, 317–341
Abstract

A cyclotomic polynomial ${\Phi }_{n}\left(x\right)$ is said to be ternary if $n=pqr$, with $p$, $q$ and $r$ distinct odd primes. Ternary cyclotomic polynomials are the simplest ones for which the behavior of the coefficients is not completely understood. Here we establish some results and formulate some conjectures regarding the coefficients appearing in the polynomial family ${\Phi }_{pqr}\left(x\right)$ with $p, $p$ and $q$ fixed and $r$ a free prime.

Keywords
ternary cyclotomic polynomial, coefficient
Primary: 11C08
Secondary: 11B83
Milestones
Received: 21 July 2010
Revised: 19 July 2011
Accepted: 15 August 2011
Published: 21 March 2012

Communicated by Kenneth S. Berenhaut
Authors
 Yves Gallot 12 bis rue Perrey 31400 Toulouse France Pieter Moree Max-Planck-Institut für Mathematik Vivatsgasse 7 D-53111 Bonn Germany Robert Wilms Sterbeckerstrasse 21 D-58579 Schalksmühle Germany