Since the celebrated Siegel-Klingen theorem on the rationality of negative partial zeta values, several works have been published providing new proofs of this theorem as well as new methods to study special values of zeta functions of totally real number fields. One such method was originated in Shintani's breakthrough article from 1976, which has been more recently reinterpreted through cohomology as the eponymous theory of Shintani cocycles. In a different direction, work in cohomological approaches to rationality theorems of special zeta values has culminated in the theory of topological polylogarithms due to Beilinson, Kings and Levin. In this article we develop both theories within a suitable framework that allows us to explicitly decompose the topological polylogarithms into Shintani cocycles, thereby clarifying the relationship between these two strands of the literature.
Julio de Mello Bezerra (Thu,) studied this question.