A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
Decomposition of elliptic multiple zeta values and iterated Eisenstein integrals
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abstract
We describe a decomposition algorithm for elliptic multiple zeta values, which amounts to the construction of an injective map $\psi$ from the algebra of elliptic multiple zeta values to a space of iterated Eisenstein integrals. We give many examples of this decomposition, and conclude with a short discussion about the image of $\psi$. It turns out that the failure of surjectivity of $\psi$ is in some sense governed by period polynomials of modular forms.
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Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.
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A construction of single-valued elliptic polylogarithms
A construction of single-valued elliptic polylogarithms on the punctured elliptic curve is given that reduces to Brown's genus-zero condition upon torus degeneration.
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Towards Motivic Coactions at Genus One from Zeta Generators
Proposes motivic coaction formulae for genus-one iterated integrals over holomorphic Eisenstein series using zeta generators, verifies expected coaction properties, and deduces f-alphabet decompositions of multiple modular values.