Criterion for Deciding Zeta-Like Multizeta Values in Positive Characteristic

Abstract

Multizeta values for F-q [theta] were initially studied by Thakur, who defined them as analogues of classical multiple zeta values of Euler. In the present article, we give an effective algorithm for determining whether a given multizeta value is zeta-like, namely, those whose ratio with the zeta value of the same weight is rational. Moreover, we state conjectures on certain families of zeta-like multizeta values. We provide the data in support of these guesses.