Ohno relation for regularized refined symmetric multiple zeta values

TL;DR

This paper extends the Ohno relation to regularized refined symmetric multiple zeta values, broadening the understanding of symmetries and relations among complex iterated integrals in number theory.

Contribution

The authors generalize Takeyama's Ohno relation for refined symmetric multiple zeta values to the regularized case, including non-admissible integrals from 0 to 0.

Findings

Established the Ohno relation for regularized refined symmetric multiple zeta values.

Extended the framework of multiple zeta value relations to non-admissible integrals.

Provided new algebraic identities linking different classes of multiple zeta values.

Abstract

The Ohno relation is one of the most celebrated results in the theory of multiple zeta values, which are iterated integrals from $0$ to $1$. In a previous paper, the authors generalized the Ohno relation to regularized multiple zeta values, which are non-admissible iterated integrals from $0$ to $1$. Meanwhile, Takeyama proved an analogue of the Ohno relation for refined symmetric multiple zeta values, which are iterated integrals from $0$ to $0$. In this paper, we generalize Takeyama's result to regularized refined symmetric multiple zeta values, which are non-admissible iterated integrals from $0$ to $0$.