Interpolated polynomial multiple zeta values of fixed weight, depth, and height

TL;DR

This paper introduces interpolated polynomial multiple zeta values, a comprehensive generalization of existing multiple zeta value variants, and computes their generating functions for fixed weight, depth, and height.

Contribution

It defines a new class of multiple zeta values that unify various existing types and derives their generating functions for specific parameters.

Findings

Unified multiple zeta value framework

Derived generating functions for fixed parameters

Connects various zeta value variants

Abstract

We define the interpolated polynomial multiple zeta values as a generalization of all of multiple zeta values, multiple zeta-star values, interpolated multiple zeta values, symmetric multiple zeta values, and polynomial multiple zeta values. We then compute the generating function of the sum of interpolated polynomial multiple zeta values of fixed weight, depth, and height.