Reciprocity laws for Legendre symbols of the type $(a+b\sqrt{m}/p)$ - Long Version

We announce a very general statement involving the rational quartic residue symbol $(m/p)_4$ and, more generally, Legendre symbols of the type ${a+b\sqrt{m}/p$. We show how our main theorem can be used to produce many older results such as Scholz's, Lehmer's or Burde's reciprocity laws and many others. It is very likely that all existing reciprocity laws of this type can be obtained from our result. This is a corrected and improved version of version 2.