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Malle's conjecture for nonic Heisenberg extensions

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arxiv 2102.09465 v1 pith:ZKFX4NUX submitted 2021-02-18 math.NT

Étienne Fouvry , Peter Koymans This is my paper · ORCID
classification math.NT
keywords extensionsheisenbergnonicconjecturemainmallemathbbalgebraic
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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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Cited by 1 Pith paper

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  1. Counterexamples for T\"urkelli's Modification on Malle's Conjecture

    math.NT 2025-02 conditional novelty 7.0 of 10

    Türkelli's modification to Malle's conjecture fails for infinite families of wreath-product groups, and a refined Malle conjecture with a corrected b-constant is proposed.

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