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An elementary proof for a theorem of Thomas and Vasquez. (English) Zbl 0853.11087
The author looks at the group of positive units in a totally real cubic field \(F\) acting on \(\mathbb{R}^3\) and gives an elementary geometric proof for the construction of a fundamental domain for this action by E. Thomas and A. Vasquez [Math. Ann. 247, 1-20 (1980; Zbl 0414.14021)]. Furthermore examples of class numbers are given as well as an explicit class number formula for a totally imaginary quadratic extension of \(F\).
Reviewer: R.Mollin (Calgary)

MSC:
11R27 Units and factorization
11R16 Cubic and quartic extensions
11R42 Zeta functions and \(L\)-functions of number fields
11R29 Class numbers, class groups, discriminants
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