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.
Meromorphic higher-ge nus integration kernels via convolution over homology cycles
6 Pith papers cite this work. Polarity classification is still indexing.
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Proves conjectural reformulation of motivic coaction and single-valued maps via zeta generators for multiple polylogarithms at genus zero on the Riemann sphere.
Single-valued polylogarithms are constructed on higher-genus once-punctured Riemann surfaces with trivial monodromy, related to prior work and used to identify the Arakelov Green's function.
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.
IterInt package evaluates iterated integrals by transforming them into solvable differential equation systems with built-in regularization.
Feynman integrals with mixed geometries (K3 surfaces, curves, points) can be computed more efficiently by extracting and using their algebraic geometric properties.
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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.