Counting algebraic integers of fixed degree and bounded height

TL;DR

This paper provides an asymptotic formula for counting algebraic integers of fixed degree over a number field with bounded Weil height, advancing understanding of their distribution.

Contribution

It introduces a new asymptotic formula for algebraic integers of fixed degree and bounded height over a number field, filling a gap in number theory.

Findings

Asymptotic count of algebraic integers with bounded height

Explicit formula involving the height parameter

Improved understanding of algebraic integers distribution

Abstract

Let $k$ be a number field. For $\mathcal{H}\rightarrow \infty$, we give an asymptotic formula for the number of algebraic integers of absolute Weil height bounded by $\mathcal{H}$ and fixed degree over $k$.