On a symmetric space attached to polyzeta values

TL;DR

This paper introduces a geometric interpretation of polyzeta values using a symmetric space and provides rapidly convergent series involving polylogarithms at 1/2 for their computation.

Contribution

It reveals a simple geometric structure underlying polyzeta values and derives quickly convergent series based on this interpretation.

Findings

Provides explicit rapidly convergent series for polyzeta numbers.

Connects polyzeta combinatorics with the square map on a symmetric space.

Offers a geometric perspective on polyzeta values.

Abstract

Quickly convergent series are given to compute polyzeta numbers. The formula involves an intricate combination of (generalized) polylogarithms at 1/2. However, the combinatorics has a very simple geometric interpretation: it corresponds with the square map on some symmetric space P.