There are consecutive cubic fields with large class numbers, when ordered by discriminant

TL;DR

This paper demonstrates that when cubic number fields are ordered by discriminant, there exist arbitrarily long sequences of fields all having class numbers exceeding any specified bound.

Contribution

It establishes the existence of arbitrarily long sequences of cubic fields with large class numbers, ordered by discriminant, highlighting new patterns in number field class number behavior.

Findings

Existence of arbitrarily long sequences of cubic fields with large class numbers

Sequences are ordered by discriminant

Class numbers exceed any given bound in these sequences

Abstract

We consider cubic number fields ordered by their discriminants, and show that there exist arbitrarily long sequences that contain only fields with class numbers greater than a given bound.