A generalization of reduced Arakelov divisors of a number field

Abstract

Let $C\ge 1$. 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 $F$.

12 pages

References in corpus (2)

• Computing Arakelov class groups
• On reduced Arakelov divisors of real quadratic fields

Cited by in corpus (1)

• Computing dimensions of spaces of Arakelov divisors of number fields