Malle's conjecture for nonic Heisenberg extensions

Étienne Fouvry; Peter Koymans

Malle's conjecture for nonic Heisenberg extensions

Number Theory 2021-03-09 v1

Authors: Étienne Fouvry , Peter Koymans

Abstract

We prove Malle's conjecture for nonic Heisenberg extensions over $\mathbb{Q}$ . Our main algebraic result shows that the number of nonic Heisenberg extensions over $\mathbb{Q}$ with discriminant bounded by $X$ is given by a character sum. We then extract the main term from this sum by exploiting oscillation of characters.

Keywords

malle's conjecture nonic heisenberg extensions discriminant character sum number fields

Cite

@article{arxiv.2102.09465,
  title  = {Malle's conjecture for nonic Heisenberg extensions},
  author = {Étienne Fouvry and Peter Koymans},
  journal= {arXiv preprint arXiv:2102.09465},
  year   = {2021}
}

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