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arXiv · 2102.09465

Malle's conjecture for nonic Heisenberg extensions

Étienne Fouvry·Peter Koymans
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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.

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Étienne Fouvry, Peter Koymans. 2021-02-18. Malle's conjecture for nonic Heisenberg extensions. https://arxiv.org/abs/2102.09465

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