Computing Arakelov class groups
Computing Arakelov class groups
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发表时间：
2008-01
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通讯作者：
R. Schoof
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作者：
R. Schoof
计算代数数域的整数环的类群和单位群的Shanks的基础结构算法和Buchmann的算法最自然地被视为Arakelov类群内的计算。本文讨论了Arakelov类群和约化Arakelov因子集的基本性质。作为应用，我们在此上下文中描述了Buchmann算法。
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.