Euler’s dilogarithm is a complex valued function given by
The dilogarithm is a special case of the polylogarithm . The Bloch–Wigner dilogarithm is defined by
The dilogarithm has remarkable relations to many areas of mathematics and mathematical physics including scissors congruence, Reidemeister’s torsion, regulators in higher algebraic K-theory, the Bloch group, CFT, Liouville's gravity?, hyperbolic geometry and cluster transformations.
Don Zagier, The dilogarithm function, in Frontiers in Number Theory, Physics, and Geometry II, pp. 3–35 (2007) MR2290758 doi:10.1007/978-3-540-30308-4 preprint pdf; Polylogarithms, Dedekind zeta functions, and the algebraic K-theory of fields, in Arithmetic Algebraic Geometry, Progr. Math. 89, Birkhäuser, Boston, 1990, 391–430 MR1085270
A. N. Kirillov, Dilogarithm identities, Progr. Theoret. Phys. Suppl. 118 (1995), 61–142 hep-th/9408113 MR1356515 doi; Identities for the Rogers dilogarithm function connected with simple Lie algebras, J. Soviet Math. 47 (1989), 2450–2458.
S. Bloch, Applications of the dilogarithm function in algebraic K-theory and algebraic geometry, in: Proc. Int. Symp. on Alg. Geometry, Kinokuniya, Tokyo 1978.