Rational deformations of the set of multiple zeta-star 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.