Selberg integral and multiple zeta values

TL;DR

This paper demonstrates that coefficients in the Taylor expansion of Selberg integrals can be expressed as linear combinations of multiple zeta values, using a beta-nbc base to ensure holomorphicity.

Contribution

It introduces a method to relate Selberg integral coefficients to multiple zeta values via a beta-nbc base, advancing understanding of their algebraic structure.

Findings

Coefficients of Selberg integrals' Taylor expansion are linear combinations of multiple zeta values.

The beta-nbc base ensures the Selberg integral's holomorphicity with respect to exponent variables.

Provides a new framework for analyzing the algebraic relations between Selberg integrals and multiple zeta values.

Abstract

In this paper, we show that the coefficient of the Taylor expansion of Selberg integrals with respect to exponent variables are expressed as a linear combination of multiple zeta values. We use beta-nbc base so that the Selberg integral is holomorphic with respect to the exponent variables.