The product structure also explains the classical Euler product for the zeta function. The zeta function of D corresponds to a Cartesian product of zeta functions of the factors, computed above as so that where the right side is a Cartesian product. Applying the isomorphism which sends t in the kth factor to , we obtain the usual Euler product.
The product structure also explains the classical Euler product for the zeta function. The zeta function of D corresponds to a Cartesian product of zeta functions of the factors, computed above as so that where the right side is a Cartesian product. Applying the isomorphism which sends t in the kth factor to , we obtain the usual Euler product.