Asymptotics for $6$-torsion and $D_6$-extensions
Number Theory
2025-12-29 v1
Abstract
We prove a composite case of the Cohen--Lenstra--Gerth heuristics. Specifically, we establish an asymptotic for the average -torsion of the class group of quadratic number fields. We also prove Malle's conjecture for Galois -extensions.
Keywords
Cite
@article{arxiv.2512.21920,
title = {Asymptotics for $6$-torsion and $D_6$-extensions},
author = {Peter Koymans and Robert J. Lemke Oliver and Efthymios Sofos and Frank Thorne},
journal= {arXiv preprint arXiv:2512.21920},
year = {2025}
}
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29 pages