Cohen–Lenstra–Martinet–Malle conjecture for even-degree class groups

Let KK be a nowhere-evenly-ramified number field of even degree nn with real signature (r1,r2)(r_1,r_2). Enumerate such fields by discriminant. Cohen–Lenstra–Martinet–Malle conjecture. The average value of the size of the 22-torsion subgroup of the class group is

#Cl(K)[2]=1+221r1r2.\#\operatorname{Cl}(K)[2]=1+2\cdot 2^{1-r_1-r_2}.

This prediction concerns the exceptional even-degree setting of nowhere-evenly-ramified fields and is part of the Cohen–Lenstra–Martinet–Malle heuristic framework. The supplied text does not provide evidence that the prediction has been proved or disproved.

Sources & referencesView supporting material

Primary source

Ashvin Swaminathan, “A new parametrization for ideal classes in rings defined by binary forms, and applications”, arXiv:2011.13578 (2024).

Additional references

2 papers in this index state this conjecture (2016–2020). The statement above is taken from the most recent of them; the others are arXiv:1603.06269.

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