Traces of Eichler-Brandt matrices and type numbers of quaternion orders
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.
quaternion algebra over a totally real algebraic number field
scientific article; zbMATH DE number 4061356
scientific article