论文信息 - Density of cubic field discriminants

Density of cubic field discriminants

In this paper we give a conjectural refinement of the Davenport- Heilbronn theorem on the density of cubic field discriminants. We explain how this refinement is plausible theoretically and agrees very well with computa- tional data. Let an be the number of isomorphism classes of abelian cubic fields with discrim- inant n. Let bn be the number of isomorphism classes of non-abelian cubic fields with discriminant n. The numbers an are very well understood. The numbers bn have been the subject of extensive theoretical and computational study for at least sixty years, but are less well understood. The object of this note is to contribute to the study of these bn, by bringing together the theoretical and computational literature. For � ∈ {−,+}, define g�(x) =

David P. Roberts

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