Class Field Theory states the correspondence between abelian extensions of k and congruence divisor class. In idelic language, there is a surjective map from $J_k/k^*$ to $Gal(k^{ab}/k)$ with its kernel unkonwn.

Tate's Thesis proved some functional equations and analytic continuity(with a finite character of $J_k/k^*$).

Question: Why Tate's thesis contributed to class field theory?