Remarks on E. A. Rahmanov's paper “on the asymptotics of the ratio of orthogonal polynomials”

Abstract It is pointed out that the proof of the basic result of Rahmanov's paper has a serious gap. It is documented by original sources that a statement he relied on in the proof contains a misprint, and it is shown by a counterexample that this statement (with the misprint) is, in fact, false. A somewhat weaker statement is proved true.