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

2024/08/02 by Xu, Peter
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2408.00962

Abstract

We find group cochains valued in currents giving explicit representatives for the GL₂-equivariant polylogarithm class of a torus. Based on the construction of weight-2 Eisenstein series for GL₂ 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 E²_α,β for various nonzero torsion sections (α, β).

Related

• Polylogarithms for GL₂ over totally real fields
• Eisenstein cohomology classes for GL_N over imaginary quadratic fields
• Rationality of the periods of Eisenstein series
• Periods detecting Eisenstein series and sums of L-values I
• The Chang-Skjelbred lemma and generalizations