Traces of Eichler-Brandt matrices and type numbers of quaternion orders
type: Item
instance of: scholarly article
title: Traces of Eichler-Brandt matrices and type numbers of quaternion orders
zbMATH Open document ID: 0651.12011
DOI: 10.1007/BF02837823
author: Otto Körner
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1987-01-01T00:00:00Z
review text: Let A be a totally definite quaternion algebra over a totally real algebraic number field and M be the ring of algebraic integers of F. For any M-order G of A formulas are derived for the mass m(G) and the type number t(G) and for the trace of the Eichler-Brandt matrix B(G,J) (where J is an integral ideal) in terms of genus invariant of G and of invariants of F and J. Thus earlier results of Eichler and others are generalized. The proofs use integration on some quotient spaces of the idele group of A and an elementary version of Selberg's trace formula.
Mathematics Subject Classification ID: 11R52
Mathematics Subject Classification ID: 11E41
Mathematics Subject Classification ID: 16H05
zbMATH DE Number: 4061356
zbMATH Keywords: class number
zbMATH Keywords: quaternion algebra over a totally real algebraic number field
zbMATH Keywords: order
zbMATH Keywords: Eichler-Brandt matrix
zbMATH Keywords: idele group
zbMATH Keywords: Selberg's trace formula
reviewed by: Meinhard Peters
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4061356