  In this paper, we construct a new Eisenstein cocycle called the
Shintani-Barnes cocycle which specializes in a uniform way to the values of the
zeta functions of general number fields at positive integers. Our basic
strategy is to generalize the construction of the Eisenstein cocycle presented
in the work of Vlasenko and Zagier by using some recent techniques developed by
Bannai, Hagihara, Yamada, and Yamamoto in their study of the polylogarithm for
totally real fields. We also closely follow the work of Charollois, Dasgupta,
and Greenberg. In fact, one of the key ingredients in this paper which enables
us to deal with general number fields is the introduction of a new technique
called the ``exponential perturbation'' which is a slight modification of the
Q-perturbation studied in their work.
