Asymptotic frequency conjecture for non-split prime-power conductors

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Let K=Q(d)K=\mathbb{Q}(\sqrt{d}) be a quadratic field with d≡2(mod3)d\equiv 2\pmod 3 and 33-class rank ϱ=0\varrho=0. Consider 33-admissible non-split prime or prime-power conductors f=qf=q, f=3f=3, and f=9f=9. Prime-power conductor frequency conjecture. The relative frequency of nilets decreases from 73%73\% through 72%72\% and 71%71\% to 69%69\%, while the relative frequency of singlets increases from 27%27\% through 28%28\% and 29%29\% to 31%31\%; all singlets have permanent type ε\varepsilon, and the final percentages for 0<dL<1070<d_L<10^7 should be close to their asymptotic limits. The claim is an experimental asymptotic prediction based on the computed ranges.

References

Primary source

Daniel C. Mayer, “Classifying multiplets of totally real cubic fields”, arXiv:2102.12187 (2021).

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