Biquadratic reciprocity laws
Ezra A. Brown · Proceedings of the American Mathematical Society · 1973
Let $p \equiv q \equiv 1\;(\bmod 4)$ be distinct primes such that $(p|q) = 1$, and let $g = [k,2m,n]$ be a binary quadratic form of determinant q which represents p. Subject to certain restrictions on k and q, we obtain some reciprocity laws for the fourth-power residue symbols ${(p|q)_4}$ and ${(q|p)_4}$.