Denert, M. The genus zeta function of hereditary orders in central simple algebras over global fields. (English) Zbl 0687.16003 Math. Comput. 54, No. 189, 449-465 (1990). 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 Cited in 11 Documents 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 Keywords:genus zeta function; local hereditary order; central simple algebra; local field; computer PDFBibTeX XMLCite \textit{M. Denert}, Math. Comput. 54, No. 189, 449--465 (1990; Zbl 0687.16003) Full Text: DOI