6533b7d8fe1ef96bd126a411
RESEARCH PRODUCT
Evaluating Multiple Polylogarithm Values at Sixth Roots of Unity up to Weight Six
Johannes M. HennVladimir A. SmirnovAlexander V. Smirnovsubject
High Energy Physics - TheoryNuclear and High Energy PhysicsPolylogarithmRoot of unityFOS: Physical sciencesFeynman graph01 natural sciencesCombinatoricsHigh Energy Physics - Phenomenology (hep-ph)0103 physical sciencesFOS: Mathematicslcsh:Nuclear and particle physics. Atomic energy. RadioactivityNumber Theory (math.NT)0101 mathematicsLinear combinationMathematical PhysicsPhysicsMathematics - Number Theory010308 nuclear & particles physicsLinear space010102 general mathematicsZero (complex analysis)Mathematical Physics (math-ph)High Energy Physics - PhenomenologyHigh Energy Physics - Theory (hep-th)lcsh:QC770-798description
We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form $G(a_1,\ldots,a_w;1)$ where the indices $a_i$ are equal to zero or a sixth root of unity, with $a_1\neq 1$. For $w\leq 6$, we present bases of the linear spaces generated by the real and imaginary parts of $G(a_1,\ldots,a_w;1)$ and present a table for expressing them as linear combinations of the elements of the bases.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2017-06-01 |