Let K be an imaginary quadratic field with fundamental discriminant \(d_K\) and \(C(\tau )\) be the Ramanujan’s cubic continued fraction. We prove in this note that if \(d_K\equiv 5\pmod {8}\) , then the values \(2^{2/3}C(\tau ), 2^{1/3}C(\tau /2), 2^{2/3}C(\tau /3)\) , and \(2^{1/3}C(\tau /6)\) are algebraic units all some \(\tau \in K\) in the complex upper half-plane \(\mathbb {H}\) . We also construct ray class fields modulo 2 over K using \(C^3(\tau )\) under certain conditions on \(\tau \in K\cap \mathbb {H}\) . Our results complement those of Cho, Koo, and Park and, more recently, of Akkarapakam and Morton on the generators of ray class fields over K involving some values of \(C(\tau )\) .
