Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces

TL;DR

This paper employs Szenes formula to compute multiple Bernoulli series, enabling the calculation of volumes of moduli spaces of flat bundles over surfaces and related multiple zeta values.

Contribution

It introduces a method to compute Witten series for classical Lie algebras using Szenes formula, linking Bernoulli series to geometric and number-theoretic quantities.

Findings

Computed volumes of moduli spaces of flat bundles over surfaces.

Connected multiple Bernoulli series to Witten series and moduli space volumes.

Provided explicit formulas for classical Lie algebras.

Abstract

Using Szenes formula for multiple Bernoulli series we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also certain multiple zeta values.