Explicit counting of integral ideals in number fields using geometry of numbers

Speaker: Anton Fehnker, KU

How many integral ideals are there in a number field with norm bounded by some constant t? In this talk we will see how to restate this question as a problem in lattice theory and present various techniques that can be used to get strong, explicit estimations. We will cover both general techniques from lattice theory, such as ways of estimating the number of lattice points in a given domain, as well as techniques that relate more explicitly to ideal lattices in Minkowski space, such as Schmidt's partition trick.