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

Published 26 Dec 2025 in math.NT | (2512.21920v1)

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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