## On the height of solutions to norm form equations

### Volume 183 / 2018

Acta Arithmetica 183 (2018), 385-396
MSC: 11J25, 11R27, 11S20.
DOI: 10.4064/aa170907-18-2
Published online: 9 April 2018

#### Abstract

Let $k$ be a number field. We consider norm form equations associated to a full $O_k$-module contained in a finite extension field $l$. It is known that the set of solutions is naturally a union of disjoint equivalence classes of solutions. We prove that each nonempty equivalence class of solutions contains a representative with Weil height bounded by an expression that depends on parameters defining the norm form equation.