The elliptic modular function $j(\tau)$ is an automorphic function on the complex upper half plane \(\bf H\) with respect to the modular group ${\it SL}_2 ({\bf Z})$. It has many applications to number theory. Starting from the hypergeometric function of 2-variables, we can construct explicit modular functions on ${\bf B}^2$ (the 2-dimensional hyper ball). They are called Picard modular functions. It is one typical way to have 2-dimensional analogs of $j(\tau)$, another one is the Hilbert modular function. In this talk we explain one Picard modular function and its application to the complex multiplication theory of higher degree. [<6>]