有限多重ゼータ値 (Various aspects of multiple zeta values)

Abstract

We give an overview of the "finite multiple zeta values" in the sense of Zagier, who has introduced a new framework of considering the "mod p multiple harmonic sums" studied by Hoffman and Zhao among others since ten years. We present a conjecture predicting a connection between finite multiple zeta values and ordinary multiple zeta values, by defining a real counterpart ("symmetric multiple zeta value" or "finite real multiple zeta value") of the finite multiple zeta value, and give some results and conjectures concerning relations among finite (and symmetric) multiple zeta values, which are analogous to the known relations in the theory of ordinary multiple zeta values. Several properties of the symmetric multiple zeta values are also given.