Jumps of ternary cyclotomic coefficients
Volume 163 / 2014
Acta Arithmetica 163 (2014), 203-213
MSC: 11B83, 11C08.
DOI: 10.4064/aa163-3-2
Abstract
It is known that two consecutive coefficients of a ternary cyclotomic polynomial $\varPhi _{pqr}(x)= \sum _k a_{pqr}(k)x^k$ differ by at most one. We characterize all $k$ such that $|a_{pqr}(k)-a_{pqr}(k-1)|=1$. We use this to prove that the number of nonzero coefficients of the $n$th ternary cyclotomic polynomial is greater than $n^{1/3}$.
