The maximal coefficient of ternary cyclotomic polynomials with one free prime

作者：Duda Dominik^*

来源：International Journal of Number Theory, 2014, 10(4): 1067-1080.

DOI：10.1142/S1793042114500158

• Ternary cyclotomic polynomial
• cyclotomic coefficient
• Kaplan's lemma
• maximal coefficient

A cyclotomic polynomial Phi(n) (x) is said to be ternary if n = pqr, with p, q and r distinct odd primes. Let M(p, q) be the maximum (in absolute value) coefficient appearing in the polynomial family Phi(pqr) (x) with p < q < r, p and q fixed. Here a stronger version of the main conjecture of Gallot, Moree and Wilms regarding M(p, q) is established. Furthermore it is shown that there is an algorithm to compute M(p) := max{M(p, q) : q > p}. Our methods are the most geometric used so far in the study of ternary cyclotomic polynomials.

• 出版日期2014-6