Computing Arakelov class groups

Abstract

Shanks's infrastructure algorithm and Buchmann's algorithm for computing class groups and unit groups of rings of integers of algebraic number fields are most naturally viewed as computations inside Arakelov class groups. In this paper we discuss the basic properties of Arakelov class groups and of the set of reduced Arakelov divisors. As an application we describe Buchmann's algorithm in this context.

41 pages

Cited by in corpus (8)

• Computing Igusa class polynomials
• Invariant generalized ideal classes -- structure theorems for p-class groups in p-extensions
• Genus theory and $\epsilon$-conjectures on p-class groups
• Well-Rounded ideal lattices of cyclic cubic and quartic fields
• On reduced Arakelov divisors of real quadratic fields
• Computing dimensions of spaces of Arakelov divisors of number fields
• A generalization of reduced Arakelov divisors of a number field
• Algorithmic enumeration of ideal classes for quaternion orders