Traces of Eichler-Brandt matrices and type numbers of quaternion orders. (English) Zbl 0651.12011

Körner, Otto

Proc. Indian Acad. Sci., Math. Sci. (Ramanujan Birth Centenary Volume) 97, No. 1-3, 189-199 (1987).

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.

Reviewer: M.Peters

MSC:

11R52	Quaternion and other division algebras: arithmetic, zeta functions
11E41	Class numbers of quadratic and Hermitian forms
16H05	Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.)

Keywords:

class number; quaternion algebra over a totally real algebraic number field; order; Eichler-Brandt matrix; idele group; Selberg’s trace formula

References:

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