I'm studying now explicit formula by the "local class field theory(written by Kenkichi Iwasawa"), but there are no description of the motivation of explicit formula(or explicit reciprocity law). I write down what I understand now about explicit reciprocity law.
Hilbert symbol is the local object to reformulate the classical power residue law(e.g:quadratic reciprocity law) in more general form. But the Hilbert symbol is defined by the local Artin map which is somewhat not explicit,so one may want to describe this symbol more explicitely. So is that the motivation for the explicit reciprocity law??
I saw the symbol which is generalization of classical Hilbert symbol for general Lubin Tate totally ramified extension(adjoin section points to the local field) in the book "local class field theory". The motivation of computing this generalized symbol is the same or prolongation of that of classical Hilbert symbol?
