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arXiv · 2308.11397

Ordering of number fields and distribution of class groups

Weitong Wang
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Abstract

When p divides the ordering of Galois group, the distribution of the Sylow p-subgroup of Cl(K) is closely related to the problem of counting fields with certain specifications. Moreover, different orderings of number fields affect the answers of such questions in a nontrivial way. So, in this paper, we set up an invariant of number fields with parameters, and consider field counting problems with specifications while the parameters change as a variable. The case of abelian extensions shows that the result of counting abelian fields has a main term with parameters. The estimate of counting cubic fields with a parameter shows that infinite moment is true for some ordering but not very likely for the others.

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Weitong Wang. 2023-08-22. Ordering of number fields and distribution of class groups. https://arxiv.org/abs/2308.11397

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