The authors claim results of the kind \(\theta_3(\tau^2)^4= \theta_3(\tau)^4\), \(\Delta(\tau^2)= \Delta(\tau)\), \(J(\tau^2)= J(\tau)\) for some \(\tau\) in the upper half plane which belong to an imaginary quadratic number field. Here, \(\theta_3\) is the Jacobi theta function, \(\Delta\) is the modular discriminant, and \(J\) is the elliptic modular function, in standard notation. The reviewer believes that the paper is irreparably wrong. If true, the claim on \(J(\tau)\), for example, would imply a contradiction to the injectivity of \(J\) on the fundamental domain of the modular group. The error occurs on p. 301 in the proof of Theorem 2.1: The first two lines in the transformation of \(\theta_3(\tau)^4\) apply to the Weierstrass \(\wp\)-function with fundamental periods 1 and T2. Then, in the third line, it is implicitly used that \(\wp\) has period \(\tau\), which is not true for most of the values of \(\tau\) under consideration.