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Functional relations for elliptic polylogarithms
- Source :
- Journal of Physics A: Mathematical and Theoretical
- Publication Year :
- 2019
- Publisher :
- arXiv, 2019.
-
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.<br />Comment: 39 pages, 5 appendices, added references and corrected typos
- Subjects :
- High Energy Physics - Theory
Statistics and Probability
Class (set theory)
Bloch group
Formalism (philosophy)
General Physics and Astronomy
FOS: Physical sciences
functional relations
01 natural sciences
Prime (order theory)
Identity (mathematics)
Simple (abstract algebra)
0103 physical sciences
FOS: Mathematics
ddc:530
Number Theory (math.NT)
010306 general physics
Link (knot theory)
Mathematical Physics
Mathematics
Mathematics - Number Theory
010308 nuclear & particles physics
Statistical and Nonlinear Physics
530 Physik
Algebra
Number theory
High Energy Physics - Theory (hep-th)
Modeling and Simulation
iterated integrals
elliptic polylogarithms
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- Journal of Physics A: Mathematical and Theoretical
- Accession number :
- edsair.doi.dedup.....9f1e85d27637841edaf9155c9a586633
- Full Text :
- https://doi.org/10.48550/arxiv.1906.11857