On the greatest common divisor of two univariate polynomials. II (Q2717616)

In an earlier paper (to appear in a volume entitled ``A tribute to Alan Baker''), the author investigated the number \(A(r,s,K)\) of non-zero coefficients of the greatest common divisor of two univariate polynomials \(f\) and \(g\) with exactly \(r\) and \(s\) non-zero coefficients belonging to a field \(K\). The only case where \(A(r,s,K)\) was not evaluated was \(r=s=3\), \(\text{char} K=0\). In the present paper this exceptional case is studied. It contains several estimates of \(A(3,3,K)\) and the degree of \((f,g)\), but the details are too complicated to be reproduced here. In particular, there is a numerical example (Example 3 on p. 106), where \(A(3,3,\mathbb Q)=6\). There is a misprint in that example. The correct polynomial is \(T_2=x^{15}-27x^9+729.\)