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On the parity of ideal classes over a fixed prime
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 142, Number 1, February 2020
- pp. 139-176
- 10.1353/ajm.2020.0003
- Article
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abstract:
For real quadratic number fields, we consider the order of ideal classes of split prime ideals, $P$, whose norm is a fixed rational prime. We collect fundamental discriminants satisfying a trivial condition for $P$ to be principal, and show that for a positive density of such discriminants, the cyclic subgroup of the ideal class group generated by $P$ does not have a 2-part.