Malle’s conjecture for nonic Heisenberg extensions
[La conjecture de Malle pour les extensions noniques de type Heisenberg]
Fouvry, Étienne1 ; Koymans, Peter2
1Université Paris–Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405 Orsay (France)
2Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn (Germany)
Annales de l'Institut Fourier, Online first, 60 p.

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.

On démontre la conjecture de Malle pour les extensions de $\mathbb{Q}$ de degré $9$ et de type Heisenberg. Le principal résultat algébrique montre que le nombre de telles extensions de discriminants bornés par $X$ est donné par une somme de caractères. On extrait le terme principal en exploitant les oscillations de ces caractères.

Reçu le :
Révisé le :
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Première publication :
DOI : 10.5802/aif.3779
Classification : 11N37, 11R20, 11R34
Keywords: Malle’s conjecture, Heisenberg group
Mots-clés : Conjecture de Malle, groupe d’Heisenberg

Fouvry, Étienne  1   ; Koymans, Peter  2

1 Université Paris–Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405 Orsay (France)
2 Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn (Germany) 
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Fouvry, Étienne; Koymans, Peter. Malle’s conjecture for nonic Heisenberg extensions. Annales de l'Institut Fourier, Online first, 60 p.

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