Lethbridge Number Theory and Combinatorics Seminar: Ha Tran

Reduced ideals of a number field F have inverses of small norms and they form a finite and regularly distributed set in the infrastructure of F. Therefore, they can be used to compute the regulator and the class number of a number field. One usually applies the reduction algorithm to find them. Ideals obtained from this algorithm are called 1-reduced. There exist reduced ideals that are not 1-reduced.

We will show that these ideals have inverses of larger norms among reduced ones. Especially, we represent a sufficient and necessary condition for reduced ideals of real quadratic fields to be obtained from the reduction algorithm.