A generalization of reduced Arakelov divisors of a number field

Let C≥1C≥1. Inspired by the LLL-algorithm, we define strongly C-reduced divisors of a number field F which are generalized from the concept of reduced Arakelov divisors. Moreover, we prove that strongly C-reduced Arakelov divisors still retain outstanding properties of the reduced ones: they form a finite, regularly distributed set in the Arakelov class group and the oriented Arakelov class group of F.