Malle’s conjecture for nonic Heisenberg extensions

Key Points

• To prove Malle’s conjecture specifically for nonic Heisenberg extensions over the rationals.
• Algebraic analysis of nonic Heisenberg extensions.
• Calculation of the number of extensions with discriminant bounded by X.
• Extraction of the main term from a character sum using oscillation techniques.
• Establishment of a formula for the count of nonic Heisenberg extensions with limited discriminant.
• Identification of character sums as key elements in deriving results.