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On an effective determination of a Shintani’s decomposition of the cone $${\mathbb{R}}_ +^ n$$. (English) Zbl 0814.11055
Let $$K$$ be a totally real algebraic number field of degree $$n \geq 2$$. The author develops a method for determining a fundamental domain for the action of the group $$E^ +_ k$$ of totally positive units of $$K$$ on $$(\mathbb{R}^{ > 0})^ n$$. The method can be viewed as a modification of Buchmann’s generalization of Lagrange’s algorithm, and it yields generators for $$E^ +_ k$$ as a by-product. The computations are carried out in the maximal real subfield of the field of 11-th roots of unity as an example.
Reviewer: M.Pohst (Berlin)

##### MSC:
 11R42 Zeta functions and $$L$$-functions of number fields
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