In this paper, we will introduce a new algebraic system called the elliptic complex, and consider the distribution of zeros of the function $L(s,\chi )$ in the corresponding complex plane. The key to this article is to discover the limiting case of the Generalized Riemann Hypothesis on elliptic complex fields and, taking a series of elliptic complex fields as variables, to study the ordinary properties of their distributions about the non-trivial zeros of $L(s,\chi )$. It is on the basis of these considerations that we will draw the following conclusions. First, the zeros of the function $L(s,\chi )$ on any two elliptic complex planes correspond one-to-one. Then, all non-trivial zeros of the $L(s,\chi )$ function on each elliptic complex plane are distributed on the critical line $\mathrm{\Re }(s)=\frac{1}{2}$ due to the critical case of the Generalized Riemann Hypothesis. Ultimately we proved the Generalized Riemann Hypothesis.