On the “gap” in a theorem of Heegner

AbstractIn 1952, Kurt Heegner gave a proof of the fact that there are exactly nine complex quadratic fields of class-number one. His proof rests on the fact that a certain 24th degree polynomial with rational coefficients has a 6th degree factor which also has rational coefficients. Unfortunately, this reducibility has never been justified. In this paper, we fill this gap in Heegner's proof