  In one of his papers, using arguments about l-adic representations, Taniyama
expresses the zeta function of an abelian variety over a number field as an
infinite product of modified Artin L-functions. The latter can be further
decomposed as products of modified Dedekind zeta functions. After recalling
Taniyama's work, we give a simple geometric proof of the resulting product
formula for abelian and more general group schemes.
