ON THE EULER PRODUCT OF THE DEDEKIND ZETA FUNCTION

It is well known that the Euler product formula for the Riemann zeta function zeta(s) is still valid for R(s) = 1 and s not equal 1. In this paper, we extend this result to zeta functions of number fields. In particular, we show that the Dedekind zeta function zeta(k)(s) for any algebraic number field k can be written as the Euler product on the line R(s) = 1 except at the point s = 1. As a corollary, we obtain the Euler product formula on the line R(s) = 1 for Dirichlet L-functions L(s, chi) of real characters.