Scholz's reciprocity law
In mathematics, Scholz's reciprocity law is a reciprocity law for quadratic residue symbols of real quadratic number fields discovered by and rediscovered by.Statement
Suppose that p and q are rational primes congruent to 1 mod 4 such that the Legendre symbol is 1. Then the ideal factorizes in the ring of integers of Q as =??' and similarly =??' in the ring of integers of Q.
Write εp and εq for the fundamental units in these quadratic fields. Then Scholz's reciprocity law says that
where is the quadratic residue symbol in a quadratic number field.
