Perturbations of the Spence-Abel equation and deformations of the   dilogarithm function
  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). 
Tobias Hartnick and Andreas Ott
math.NT math.CA math.GR