Zeta-like multizeta values for mathbb{F}_q [t]

We prove and conjecture several relations between multizeta values for F _q [t], focusing on the zeta-like values, namely those whose ratio with the zeta value of the same weight is rational (or equivalently algebraic). In particular, we describe them conjecturally fully for q = 2, or more generally for any q for ‘even’ weight (‘eulerian’ tuples). We provide some data in support of the guesses.