  We define the class of normalized Shintani L-functions of several variables.
Unlike Shintani zeta functions, the normalized Shintani L-function is a
holomorphic function. Moreover it satisfies a good functional equation. We show
that any Hecke L-function of a totally real field can be expressed as a
diagonal part of some normalized Shintani L-function of several variables. This
gives a good several variables generalization of a Hecke L-function of a
totally real field. This also gives a new proof of the functional equation of
the Hecke L-function of a totally real field.
