Cubic residuacity of real quadratic integers

Ron Evans; Mark Van Veen

Cubic residuacity of real quadratic integers

Number Theory 2025-11-18 v1

Authors: Ron Evans , Mark Van Veen

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.

Keywords

real quadratic integers cubic residuacity form class group prime residues cubic norm

Cite

@article{arxiv.2511.12513,
  title  = {Cubic residuacity of real quadratic integers},
  author = {Ron Evans and Mark Van Veen},
  journal= {arXiv preprint arXiv:2511.12513},
  year   = {2025}
}

Comments

8 pages

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