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Some applications of the quasi-Riemann hypothesis to class groups and small generators of number fields
Abstract
We prove an effective version of the Chebotarev density theorem, conditional on the quasi-Riemann hypothesis for the Dedekind zeta function. Drawing on recent breakthroughs of OpenAI and Cureton--Thorner, we make unconditional the Ellenberg--Venkatesh bounds on ℓ-torsion in class groups of number fields and extend an averaged result of Lemke Oliver--Smith to arbitrary families of degree-d-fields. Further applications are given to the least prime splitting and to small generators in number fields.
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BibTeX
@misc{frei2026some,
title = {{Some applications of the quasi-Riemann hypothesis to class groups and small generators of number fields}},
author = {Christopher Frei and Efthymios Sofos and Martin Widmer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18491},
eprint = {2610.18491},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18491},
}
RIS
TY - UNPB
TI - Some applications of the quasi-Riemann hypothesis to class groups and small generators of number fields
AU - Christopher Frei
AU - Efthymios Sofos
AU - Martin Widmer
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.18491
UR - https://arxiv.org/abs/2610.18491
AB - We prove an effective version of the Chebotarev density theorem, conditional on the quasi-Riemann hypothesis for the Dedekind zeta function. Drawing on recent breakthroughs of OpenAI and Cureton--Thorner, we make unconditional the Ellenberg--Venkatesh bounds on ℓ-torsion in class groups of number fields and extend an averaged result of Lemke Oliver--Smith to arbitrary families of degree-d-fields. Further applications are given to the least prime splitting and to small generators in number fields.
ER -