A generalization of reduced Arakelov divisors of a number field

Let \(C \geq 1\). 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 \(F\).