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

Peter Xu

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arXiv · 2408.00962

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

Peter Xu

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Abstract

We find group cochains valued in currents giving explicit representatives for the $\text{GL}_2$-equivariant polylogarithm class of a torus. Based on the construction of weight-$2$ Eisenstein series for $\text{GL}_2$ 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 $E^2_{\alpha,\beta}$ for various nonzero torsion sections $(\alpha, \beta)$.

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Peter Xu. 2024-08-02. Classical periods of Eisenstein series and Bernoulli polynomials in the equivariant cohomology of a torus. https://arxiv.org/abs/2408.00962

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