On algebra of big zeta values

TL;DR

This paper introduces an algebra of big zeta values, bridging multiple zeta values and periods of the multiple zeta motive, and provides methods to express these periods in terms of multiple zeta values.

Contribution

It defines a new algebraic structure called big zeta values, linking them to moduli space periods and offering an algorithm to express these as multiple zeta values.

Findings

Big zeta values are periods of the moduli space of genus zero curves.

Convergent big zeta values can be expressed as rational combinations of multiple zeta values.

Provides an alternative proof and algorithm for expressing periods as multiple zeta values.

Abstract

The algebra of big zeta values we introduce in this paper is an intermediate object between multiple zeta values and periods of the multiple zeta motive. It consists of number series generalizing multiple zeta values, the simplest examples, which are not multiple zeta series, are Tornheim sums. We show that convergent big zeta values are periods of the moduli space of stable curves of genus zero on one hand and multiple zeta values on the other hand. It gives an alternative way to prove that any such period may be expressed as a rational linear combination of multiple zeta values and a simple algorithm for finding such an expression.