Duality relations are deduced for tails of multiple zeta values using elementary methods. These formulas extend the classical duality formulas for multiple zeta values. 2000 AMS Classi cation Numbers: 33C20.

If true, this property would mean that there is no interesting algebraic structure. There are very few results on the arithmetic nature of these numbers, even less on their independence: it is known that π is a transcendental numbers, hence, so are all ζ(2n), n ≥ 1. It is also known that ζ(3) is irrational (Apéry, 1978), and that infinitely many ζ(2n+ 1) are irrational (further sharper results ...

The structure of tree–level open and closed superstring amplitudes is analyzed. For the open superstring amplitude we find a striking and elegant form, which allows to disentangle its α–expansion into several contributions accounting for different classes of multiple zeta values. This form is bolstered by the decomposition of motivic multiple zeta values, i.e. the latter encapsulate the α–expan...

We refine a formula on values of multiple sine functions at division points. As applications we prove a formula on a sum of reciprocal trigonometric values, and obtain multiple modularity of a three variable modular function, which concerns a generalization of the Dedekind η function.

Multiple zeta values (MZVs, also called Euler sums or multiple harmonic series) are nested generalizations of the classical Riemann zeta function evaluated at integer values. The fact that an integral representation of MZVs obeys a shuffle product rule allows the possibility of a combinatorial approach to them. Using this approach we prove a longstanding conjecture of Don Zagier about MZVs with...

Abstract. In this paper we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζq(s1, . . . , sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang [12] on the renormalization of Euler-Zagier multiple zeta values. We show that our renormalization process pr...