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      Perturbations of the Spence-Abel equation and deformations of the dilogarithm function

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          Abstract

          We analyze existence, uniqueness and regularity of solutions for perturbations of the Spence-Abel equation for the Rogers' dilogarithm. As an application we deduce a version of Hyers-Ulam stability for the Spence-Abel equation. Our analysis makes use of a well-known cohomological interpretation of the Spence-Abel equation and is based on our recent results on continuous bounded cohomology of SL(2,R).

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          Journal
          1601.07109

          Number theory,Algebra
          Number theory, Algebra

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