The flatness of a class of ternary cyclotomic polynomials

Recently, there has been much progress in our understanding of the flatness of ternary cyclotomic polynomials, but a complete classification is not known. Let $p＜q＜r$ be odd primes such that $q\equiv\pm1\pmod p$ and $zr\equiv\pm1\pmod{pq}$. The cases $1\leq z\leq 6$ have been thoroughly investigated. In this paper, we concentrate on the case $z=7$, giving a classification of the cases for which $A(pqr)=1$. We also present some results about the coefficients of $\Phi_{pqr}(x)$ for the general cases of $z$.