$t$-adic symmetric multiple zeta values for indices in which $1$ and $3$ appear alternately

TL;DR

This paper studies a specific class of symmetric multiple zeta values with alternating 1s and 3s, exploring their expressibility as polynomials in Riemann zeta values and providing explicit formulas.

Contribution

It offers a conjecturally complete list of explicit formulas for symmetric multiple zeta values with alternating 1s and 3s, expanding understanding of their algebraic structure.

Findings

Identification of symmetric multiple zeta values expressible as Riemann zeta polynomials

Explicit formulas for these special zeta values

Conjectural completeness of the list of formulas

Abstract

We consider the symmetric multiple zeta values in $\mathcal{S}_m$ without modulo $\pi^2$ reduction for indices in which $1$ and $3$ appear alternately. We investigate those values that can be expressed as a polynomial of the Riemann zeta values, and give a conjecturally complete list of explicit formulas for such values.