Cyclotomic symmetric multiple zeta values span the space of cyclotomic multiple zeta values

TL;DR

This paper proves that cyclotomic symmetric multiple zeta values form a basis for the space of cyclotomic multiple zeta values modulo i, clarifying their algebraic structure and relationships.

Contribution

It establishes that cyclotomic symmetric multiple zeta values span the entire space of cyclotomic multiple zeta values modulo i, providing a new understanding of their algebraic relations.

Findings

Cyclotomic symmetric multiple zeta values span the space of cyclotomic multiple zeta values.

The result holds modulo i, indicating a specific algebraic equivalence.

Supports the conjecture that symmetric multiple zeta values form a basis for the cyclotomic case.

Abstract

In this paper, we show that the cyclotomic symmetric multiple zeta values, independently proposed by Jarossay, Singar and Zhao, and Tasaka, span the space of the cyclotomic multiple zeta values modulo $\pi i$.