Will Hansen

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math.NT2026

Counting quaternion extensions by multi-heights

Willem Hansen

We prove a case of a conjecture of Gundlach on the number of Galois extensions over $\QQ$ with bounded multi-invariants for the group $G = Q_{8}$ . We also obtain results when imposing…

math.NT2025

Counting $D_{4}$ -field extensions by multi-invariants

Willem Hansen, Anna Zanoli

We count the number of Galois extensions $M / Q$ with fixed Galois group $Gal (M / Q) = D_{4}$ ordered by multi-invariants introduced by Gundlach. We verify the asy…

Counting quaternion extensions by multi-heights

Counting D4​-field extensions by multi-invariants

Counting $D_{4}$ -field extensions by multi-invariants