Singular values of some modular functions and their applications to class fields (Q954796)

For a positive integer \(N\) greater than \(7\), Let \(K_{(N)}\) be the ray class field of modulus \(N\) of an imaginary quadratic filed \(K\). By using the results of \textit{N. Ishida} and \textit{N. Ishii} [Tokyo J. Math. 22, No. 1, 167--175 (1999; Zbl 0944.11020)] and \textit{I. Chen} and \textit{N. Yui} [Ohio State Univ. Math. Res. Inst. Publ. 4, 255--326 (1996; Zbl 0918.11024)], the authors show as one of main results that \(K_{(N)}\) is generated by singular values of at most two modular functions which are products of Klein forms and are generators of the modular function field with respect to the group \(\Gamma_1(N)\). Further they give one modular function such that its singular value generates a ring class field of which conductor is a divisor of 5.