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The genus zeta function of hereditary orders in central simple algebras over global fields. (English) Zbl 0687.16003

The author derives an explicit method for calculating the genus zeta function of any local hereditary order in a central simple algebra over a local field. This genus zeta function is obtained as a finite sum of explicit terms which can be calculated with a computer, and for which the author gives examples and remarks on the programming.
Reviewer: R.A.Mollin

MSC:

16H05 Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)
11S40 Zeta functions and \(L\)-functions
12-03 History of field theory
11M35 Hurwitz and Lerch zeta functions
16Kxx Division rings and semisimple Artin rings
16P10 Finite rings and finite-dimensional associative algebras
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