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

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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+2⋅21−r1−r2.\#\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.

References

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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