Analytic continuation of Kochubei multiple polylogarithms and its applications

TL;DR

This paper develops an analytic continuation method for Kochubei multiple polylogarithms, establishing new linear relations and independence results for their values at algebraic points from a cohomological perspective.

Contribution

It introduces an analytic continuation technique for Kochubei polylogarithms and proves new linear relations and independence results at algebraic points.

Findings

Established an analytic continuation for Kochubei multiple polylogarithms.

Derived a family of linear relations among these polylogarithm values.

Proved linear independence results at algebraic elements from a cohomological viewpoint.

Abstract

In the present paper, we propose an analytic continuation of Kochubei multiple polylogarithms using the techniques developed by Furusho. Moreover, we produce a family of linear relations and a linear independence result for values of our analytically continued Kochubei polylogarithms at algebraic elements from a cohomological aspect.