The Equidistribution of Lattice Shapes of Rings of Integers of Cubic, Quartic, and Quintic Number Fields

The concept of the equidistribution of lattice shapes of rings of integers in number fields, including cubic, quartic, and quintic fields, pertains to the distribution of the shapes of lattices associated with these algebraic structures in relation to an appropriate measure. Here, "lattice shapes" refers to the geometric and arithmetic properties of the rings of integers in these number fields, which can be analyzed in terms of their embeddings and their discriminants. ### Overview of the Concepts 1.