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  Functional relations for elliptic polylogarithms

Brödel, J., & Kaderli, A. (in preparation). Functional relations for elliptic polylogarithms.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0004-70BB-B Version Permalink: http://hdl.handle.net/21.11116/0000-0004-70DB-7
Genre: Paper

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1906.11857.pdf (Preprint), 924KB
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 Creators:
Brödel, Johannes1, Author              
Kaderli , Andre, Author
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: High Energy Physics - Theory, hep-th,Mathematics, Number Theory, math.NT
 Abstract: Numerous examples of functional relations for multiple polylogarithms are known. For elliptic polylogarithms, however, tools for the exploration of functional relations are available, but only very few relations are identified. Starting from an approach of Zagier and Gangl, which in turn is based on considerations about an elliptic version of the Bloch group, we explore functional relations between elliptic polylogarithms and link them to the relations which can be derived using the elliptic symbol formalism. The elliptic symbol formalism in turn allows for an alternative proof of the validity of the elliptic Bloch relation. While the five-term identity is the prime example of a functional identity for multiple polylogarithms and implies many dilogarithm identities, the situation in the elliptic setup is more involved: there is no simple elliptic analogue, but rather a whole class of elliptic identities.

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 Dates: 2019-06-27
 Publication Status: Not specified
 Pages: 39 pages, 5 appendices
 Publishing info: -
 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1906.11857
URI: http://arxiv.org/abs/1906.11857
 Degree: -

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