Abstract

We establish how the spectral decomposition for a Riemann surface determines the allocation of the bounded cohomology over the representations of SL2(R). Then we explore the connections of the Dilogarithm with the continuous bounded cohomology of SL2(R) and SL2(C). In particular, it appears that Rogers' Dilogarithm is uniquely determined even measurably by the Spence–Abel functional equation.

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