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

A cyclotomic polynomial Φn(x) 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 Φpqr(x) with p < q < r, p and q fixed and r a free prime.

ternary cyclotomic polynomial, coefficient
Mathematical Subject Classification 2000
Primary: 11C08
Secondary: 11B83
Received: 21 July 2010
Revised: 19 July 2011
Accepted: 15 August 2011
Published: 21 March 2012

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