Bin Zhang: The upper bound of a class of ternary cyclotomic polynomials , p. 25-32

Abstract:

Let $A_{+}(n)$ denote the largest coefficients of $n$-th cyclotomic polynomial $\Phi_n(x)$. Let $w>1$ be an integer and $p<q<r$ be odd primes such that $p\equiv1\pmod w$, $q\equiv 1\pmod {pw}$ and $r\equiv w\pmod {pq}$. In this paper, we prove that $A_{+}(pqr)=1$.

Key Words: cyclotomic polynomial; ternary cyclotomic polynomial; upper bounds of cyclotomic polynomial.

2010 Mathematics Subject Classification: Primary 11B83, Secondary 11C08