Ohno relation for regularized multiple zeta values

TL;DR

This paper extends the Ohno relation, a symmetry property of multiple zeta values, to regularized versions by explicitly relating their values at dual indices through gamma functions.

Contribution

It generalizes the Ohno relation to regularized multiple zeta values, providing explicit formulas involving gamma functions.

Findings

The operator's relation between indices and duals is expressed explicitly.

The generalized relation involves gamma functions, unlike the original invariance.

The paper broadens understanding of symmetries in regularized multiple zeta values.

Abstract

The Ohno relation for multiple zeta values can be formulated as saying that a certain operator, defined for indices, is invariant under taking duals. In this paper, we generalize the Ohno relation to regularized multiple zeta values by showing that, although the suitably generalized operator is not invariant under taking duals, the relation between its values at an index and at its dual index can be written explicitly in terms of the gamma function.