The paper proves the average size of 2-torsion in class groups is 2 for one 3-adic ramification family of pure cubic fields and 3/2 for the other, and attributes the split to Hecke reciprocity.
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Hecke reciprocity and class groups
The paper proves the average size of 2-torsion in class groups is 2 for one 3-adic ramification family of pure cubic fields and 3/2 for the other, and attributes the split to Hecke reciprocity.