Multiple polylogarithm values at roots of unity

Details Multiple polylogarithm values at roots of unity Multiple polylogarithm values at roots of unity

2008-10-06

arxiv.org/abs/0810.1064v1

C. R. Acad. Sci. Paris, Ser. I, 346 (2008) pp. 1029-1032.

Mathematics

Number Theory

A shorter version is to appear in C. R. Acad. Sci. Paris, Ser. I

Scientific paper

10.1016/j.crma.2008.09.011

For any positive integer $N$ let $\mu_N$ be the group of the $N$th roots of unity. In this note we shall study the $\Q$-linear relations among values of multiple polylogarithms evaluated at $\mmu_N$. We show that the standard relations considered by Racinet do not provide all the possible relations in the following cases: (i) level N=4, weight $w=3$ or 4, and (ii) $w=2$, $7

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