Revisiting the action of a subgroup of the modular group on imaginary quadratic number fields

Abdulaziz Deajim

Consider the modular group $\mbox{PSL}(2,\mathbb{Z})=\langle x, \, y \,|\, x^2=y^3=1\rangle$ generated by the transformations $x:z\mapsto -1/z$ and $y:z\mapsto (z-1)/z$. Let $H$ b…