Evaluating Multiple Polylogarithm Values at Sixth Roots of Unity up to Weight Six

2015/12/28 by Johannes M. Henn, Henn, Johannes M., Alexander V. Smirnov +3
Materials Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Number Theory (math.NT) #Polymer Synthesis and Characterization #hep-ph #hep-th #math-ph #math.MP #math.NT

paper · pdf · doi:10.48550/arxiv.1512.08389

15 pages, exposition improved, to appear in Nuclear Physics B

openalex publication_date 2015/12/28 · arxiv created 2017/03/27 · arxiv updated 2017/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We evaluate multiple polylogarithm values at sixth roots of unity up to weight six, i.e. of the form G(a₁,…,a_w;1) where the indices a_i are equal to zero or a sixth root of unity, with a₁≠ 1. For w≤ 6, we present bases of the linear spaces generated by the real and imaginary parts of G(a₁,…,a_w;1) and present a table for expressing them as linear combinations of the elements of the bases.

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