Zeta-integrals and transformation formulas for certain Dirichlet series

We will introduce zeta-integrals related to Shintani zeta functions, and we will show how the
former turn out to be nicer in systematizing computations involving the latter, specially in higher
dimensions. In particular, for some relevant cases, we will use these zeta-integrals to present a
sort of inversion of certain transformation formulas satisfied by some (more or less) recognizable
Fourier expansions.