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arXiv · 2512.21920

Asymptotics for $6$-torsion and $D_6$-extensions

Peter Koymans·Robert J. Lemke Oliver·Efthymios Sofos·Frank Thorne
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Abstract

We prove a composite case of the Cohen--Lenstra--Gerth heuristics. Specifically, we establish an asymptotic for the average $6$-torsion of the class group of quadratic number fields. We also prove Malle's conjecture for Galois $D_6$-extensions.

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Peter Koymans, Robert J. Lemke Oliver, Efthymios Sofos, Frank Thorne. 2025-12-26. Asymptotics for $6$-torsion and $D_6$-extensions. https://arxiv.org/abs/2512.21920

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