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On traces of the Brandt-Eichler matrices. (English) Zbl 0924.11095

The number of locally principal ideals with given norm in a class of definite quaternion orders and the traces of the Brandt-Eichler matrices corresponding to these orders are computed. As applications the number of representations of algebraic integers by norm forms of definite quaternion orders with class number one are computed. Furthermore class number relations for some CM-fields are obtained.
For a corrigendum see ibid. 29, No. 1, 321–325 (2017; Zbl 1429.11206).

MSC:

11R52 Quaternion and other division algebras: arithmetic, zeta functions
11E12 Quadratic forms over global rings and fields
11R29 Class numbers, class groups, discriminants

Citations:

Zbl 1429.11206
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References:

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