  It is known that the special values at nonpositive integers of a Dirichlet
$L$-function may be expressed using the generalized Bernoulli numbers, which
are defined by a canonical generating function. The purpose of this article is
to consider the generalization of this classical result to the case of Hecke
$L$-functions of totally real fields. Hecke $L$-functions may be expressed
canonically as a finite sum of zeta functions of Lerch type. By combining the
non-canonical multivariable generating functions constructed by Shintani, we
newly construct a canonical class, which we call the Shintani generating class,
in the equivariant cohomology of an algebraic torus associated to the totally
real field. Our main result states that the specializations at torsion points
of the derivatives of the Shintani generating class give values at nonpositive
integers of the zeta functions of Lerch type. This result gives the insight
that the correct framework in the higher dimensional case is to consider higher
equivariant cohomology classes instead of functions.
