Counting ideals in ray classes

Abstract

Let K be a number field and q an integral ideal in OK. A result of Tatuzawa [10] from 1973, computes the asymptotic (with an error term) for the number of ideals with norm at most x in a class of the narrow ray class group of K modulo q. This result bounds the error term with a constant whose dependence on q is explicit but dependence on K is not explicit. The aim of this paper is to prove this asymptotic with a fully explicit bound for the error term.