The quantum ${\mathfrak g}_2$ invariant and relations of multiple zeta values

Abstract

In this paper we obtain a family of relations among the multiple zeta values by calculating the quantum [Formula: see text]-invariant of a framed oriented link, where Γ1,0 is the 7-dimensional irreducible representation of the exceptional simple Lie algebra [Formula: see text] over [Formula: see text].

Signed $q$-analogs of Tornheim's double series

“…have attracted increasing attention in recent years; see eg. [2,3,4,5,6,8,9,10,11,13,16,24,26,27,29,30,31]. The survey articles [7,18,19,36,37,38] provide an extensive list of references.…”

The distribution of Manin's iterated integrals of modular forms

“…3] and certain aspects of the theory of multiple zeta-values (see [30] and the references therein, [23,12,21,23,24,25]). The theory has fascinating connections to physics [8], mixed Tate motives [26,9,10], deformation quantization [39,1], knot invariants [43,42,33] and many other areas.…”