Classical periods of Eisenstein series and Bernoulli polynomials in the equivariant cohomology of a torus

We find group cochains valued in currents giving explicit representatives for the GL₂ GL 2 -equivariant polylogarithm class of a torus. Based on the construction of weight-2 Eisenstein series for GL₂ GL 2 from this polylogarithm class, we give a geometrically-flavored derivation of the classical formulas for the associated Dedekind-Rademacher homomorphisms, i.e. the periods of E²α ,β E α , β 2 for various nonzero torsion sections (α ,β ) ( α , β ) .