Okazaki, Ryotaro On an effective determination of a Shintani’s decomposition of the cone \({\mathbb{R}}_ +^ n\). (English) Zbl 0814.11055 J. Math. Kyoto Univ. 33, No. 4, 1057-1070 (1993). 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) Cited in 1 ReviewCited in 7 Documents MSC: 11R42 Zeta functions and \(L\)-functions of number fields Keywords:Shintani decomposition; totally real field; group of totally positive units; fundamental domain; generators; modified Buchmann algorithm × Cite Format Result Cite Review PDF Full Text: DOI