  In this paper, we give an explicit formula of the Shintani double zeta
functions with any ramification in the most general setting of adeles over an
arbitrary number field. Three applications of the explicit formula are given.
First, we obtain a functional equation satisfied by the Shintani double zeta
functions in addition to Shintani's functional equations. Second, we establish
the holomorphicity of a certain Dirichlet series generalizing a result by
Ibukiyama and Saito. This Dirichlet series occurs in the study of unipotent
contributions of the geometric side of the Arthur-Selberg trace formula of the
symplectic group. Third, we prove an asymptotic formula of the weighted average
of the central values of quadratic Dirichlet $L$-functions.
