Cubic residuacity of real quadratic integers

Abstract

Given a real quadratic integer $u=A+B\sqrt{D}$ with cubic norm, we identify all the classes in a related form class group that represent primes $p$ for which $u$ is a cubic residue mod $p$. A special case of this result was conjectured in a 2025 paper of Evans, Lemmermeyer, Sun, and Van Veen.

8 pages