Algebraic number theory is a foundational branch of mathematics that investigates the properties of algebraic numbers and their relationships through the lens of field extensions and rings of integers ...

This is a preview. Log in through your library . Abstract In a quadratic number field $\mathbf{Q}(\sqrt D), D$ a squarefree integer, with class number 1, any algebraic integer can be decomposed ...

We want to decide whether given algebraic numbers satisfy an integer relation shorter than a given bound. This will be done by deciding whether a suitably chosen lattice contains a short vector, which ...