Application of Weierstrass units to relative power integral bases

TL;DR

This paper constructs relative power integral bases for specific abelian extensions of imaginary quadratic fields (excluding two special cases) using Weierstrass units, advancing number theory and algebraic number field theory.

Contribution

It introduces a novel method to explicitly construct relative power integral bases in abelian extensions of imaginary quadratic fields via Weierstrass units.

Findings

Explicit construction of relative power integral bases

Application of Weierstrass units in algebraic number theory

Extension of known methods to new classes of fields

Abstract

Let $K$ be an imaginary quadratic field other than $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-3})$. We construct relative power integral bases between certain abelian extensions of $K$ in terms of Weierstrass units.