# The shape of cubic fields

## TL;DR

This paper proves that the shapes of cubic fields become uniformly distributed as their discriminants grow, using advanced methods developed by Shintani, Taniguchi, and Thorne.

## Contribution

It establishes the quantitative equidistribution of cubic field shapes when ordered by discriminant, extending previous theoretical frameworks.

## Key findings

- Shapes of cubic fields are equidistributed in the limit.
- Quantitative bounds on the distribution are provided.
- Method extends Shintani's approach with new developments.

## Abstract

We use the method of Shintani, as developed by Taniguchi and Thorne, to prove the quantitative equidistribution of the shape of cubic fields when the fields are ordered by discriminant.