PreprintarXiv licencearXiv
Counting quaternion extensions by multi-heights
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=Q8. We also obtain results when imposing local conditions at the wildly ramified place. As an application, we prove asymptotics for the number of Q8-extensions with bounded product of ramified primes.
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BibTeX
@misc{hansen2026counting,
title = {{Counting quaternion extensions by multi-heights}},
author = {Willem Hansen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18815},
eprint = {2610.18815},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18815},
}
RIS
TY - UNPB
TI - Counting quaternion extensions by multi-heights
AU - Willem Hansen
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18815
UR - https://arxiv.org/abs/2610.18815
AB - 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.
ER -