Divided differences and complex variations of multiple zeta-star values
arXiv:2606.16627
The paper investigates the limiting behavior of finite multiple star harmonic sums by constructing a complex analytic interpolation using divided differences, analyzes its range for real arguments, and proposes an injectivity conjecture for the complex case.
Abstract
The derived set of multiple zeta-star values is the half-line . In this paper, we study the corresponding limiting set for finite multiple star harmonic sums. Using the theory of divided differences, we construct a natural complex analytic interpolation of finite multiple star harmonic sums. For real , we analyze the range of this interpolation in detail and prove a finite zeta-star correspondence. In the complex case, we formulate an injectivity conjecture, which may be viewed as the complex variation of zeta-star correspondence for multiple zeta-star values.
45 pages