Definite quaternion orders of class number one. (English) Zbl 0843.11048

It is shown that there are exactly 25 isomorphism classes of definite quaternion orders of class number one over \(\mathbb{Z}\); they are listed explicitly. It is remarkable that 23 of the orders are Gorenstein orders and 2 are non-Gorenstein orders.


11R54 Other algebras and orders, and their zeta and \(L\)-functions
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