Zeta-function of simple algebras over $\sharp$-fields

Question

What is the Zeta-function $\zeta_A$ of simple algebra over ${\Bbb Q}$ when

1. $A \colon= {\mathrm{M}}_2({\Bbb Q})$

2. $A \colon= \{{\Bbb Q} \oplus {\Bbb Q}x \oplus{\Bbb Q}y \oplus {\Bbb Q}xy\,|\,x^2 = y^2 = -1, xy = -yx\}$, i.e. an quaternion algebra over ${\Bbb Q}$.

I have difficulty for the reference.

Answer 1

Paul Garret has notes, where chapter $5$ is an appendix about zeta functions of quaternion algebras. The references contain the book Zeta Functions of Simple Algebras by R. Godement and H. Jacquet.