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

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.

23 pages