Biquadratic reciprocity laws

Brown, Ezra

doi:10.1090/S0002-9939-1973-0313172-8

Biquadratic reciprocity laws
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by Ezra Brown PDF

Proc. Amer. Math. Soc. 37 (1973), 374-376 Request permission

Abstract:

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 ${(q|p)_4}$.

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