Corrigendum to “Quantum integers and cyclotomy” [J. Number Theory 109 (1) (2004) 120–135].

One of the theorems in the original paper (Borisov, Nathanson, and Wang (2004) [1] ) only holds for polynomials and not for rational functions. We explain the mistake, and also prove a new theorem for the rational function case. [ABSTRACT FROM AUTHOR]