Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
The Galois coaction on the electron anomalous magnetic moment
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abstract
Recently S. Laporta published a partial result on the fourth order QED contribution to the electron anomalous magnetic moment $g-2$. This result contains explicit polylogarithmic parts with fourth and sixth roots of unity. In this note we convert Laporta's result into the motivic `$f$ alphabet'. This provides a much shorter expression which makes the Galois structure visible. We conjecture the $Q$ vector spaces of Galois conjugates of the QED $g-2$ up to weight four. The conversion into the $f$ alphabet relies on a conjecture by D. Broadhurst that iterated integrals in certain Lyndon words provide an algebra basis for the extension of multiple zeta values by sixth roots of unity. We prove this conjecture in the motivic setup.
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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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Deriving motivic coactions and single-valued maps at genus zero from zeta generators
Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
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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.