Computing Arakelov class groups

Details Computing Arakelov class groups Computing Arakelov class groups

2008-01-24

arxiv.org/abs/0801.3835v1

Mathematics

Number Theory

41 pages

Scientific paper

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.

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