Counting quaternion extensions by multi-heights

Willem Hansen

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arXiv · 2610.18815

Counting quaternion extensions by multi-heights

Willem Hansen

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Abstract

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 local conditions at the wildly ramified place. As an application, we prove asymptotics for the number of $Q_8$-extensions with bounded product of ramified primes.

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Willem Hansen. 2026-10-13. Counting quaternion extensions by multi-heights. https://arxiv.org/abs/2610.18815

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