On reduced Arakelov divisors of real quadratic fields

Abstract

We generalize the concept of reduced Arakelov divisors and define $C$-reduced divisors for a given number $C\ge 1$. These $C$-reduced divisors have remarkable properties which are similar to the properties of reduced ones. In this paper, we describe an algorithm to test whether an Arakelov divisor of a real quadratic field $F$ is $C$-reduced in time polynomial in $\log |{\Delta }_F|$ with ${\Delta }_F$ the discriminant of $F$. Moreover, we give an example of a cubic field for which our algorithm does not work.

18 pages

References in corpus (1)

• Computing Arakelov class groups

Cited by in corpus (2)

• Computing dimensions of spaces of Arakelov divisors of number fields
• A generalization of reduced Arakelov divisors of a number field