On standard L-functions attached to automorphic forms on definite orthogonal groups

We show an explicit functional equation of the standard L-function associat ed with an automorphic form on a definite orthogonal group over a totally r eal algebraic number field. This is a completion and a generalization of ou r previous paper, in which we constructed standard L-functions by using Ran kin-Selberg convolution and the theory of Shintani functions under certain technical conditions. In this article we remove these conditions. Furthermo re we show that the L-function of f has a pole at s = m/2 if and only if f is a constant function.