Counting integral ideals in number fields

Counting the number of integral ideals of bounded norm in a number field $K$ is a fundamental question that has been studied since the time of Dedekind and Weber. In this talk we will report on a joint work with Alessandro Languasco and Pieter Moree, where we obtain improvements in the existing results when $K$ is an abelian extension of $\mathbb{Q}$ of degree at least $4$.