Recent zbMATH articles in MSC 11E76https://www.zbmath.org/atom/cc/11E762021-04-16T16:22:00+00:00WerkzeugLinearly dependent powers of binary quadratic forms.https://www.zbmath.org/1456.110442021-04-16T16:22:00+00:00"Reznick, Bruce"https://www.zbmath.org/authors/?q=ai:reznick.bruceSummary: Given an integer \(d \ge 2\), what is the smallest \(r\) so that there is a set of binary quadratic forms \(\{f_1,\dots,f_r\}\) for which \(\{f_j^d\}\) is nontrivially linearly dependent? We show that if \(r \le 4\), then \(d \le 5\), and for \(d \ge 4\), construct such a set with \(r = \lfloor d/2\rfloor + 2\). Many explicit examples are given, along with techniques for producing others.