On the coefficients of ternary cyclotomic polynomials (Q1394911)

By ingenious estimations the author finds bounds for the size of the coefficients \(a_m\) of the ternary cyclotomic polynomials \(\Phi_{pqr}\), \(p\), \(q\), \(r\) primes, \(p< q< r\). E.g., \(|a_m|< (p-1)/2+a\), where \(a= \min (q^*,r^*,p-q^*,p-r^*)\) with \(0< q^*,r^*< p\) the inverses of \(q\) and \(r\bmod p\), respectively. Evaluating this in three corollaries, he immediately can derive all previously known estimations. Further amazing theorems are announced.