Rational deformations of the set of multiple zeta-star values

TL;DR

This paper investigates the structure of rational deformations of multiple zeta-star values using bounded variation functions, revealing their connection to fractal geometry and providing insights into their metric properties.

Contribution

It introduces a novel analysis of the derived sets of rational deformations of multiple zeta-star values through function decompositions and explores their relation to Cantor sets.

Findings

Describes the metric structure of derived sets of rational deformations.

Establishes a connection between these deformations and Cantor sets.

Provides a framework for understanding the fractal nature of these values.

Abstract

In this paper we study the derived sets for the rational deformations of multiple zeta-star values. By using the theory of bounded variation functions, we will give function decompositions which describe the metric structure of the derived sets. The connection between the rational deformation of multiple zeta-star values and the $n$-th Cantor set in fractal geometry is also discussed.