A generalized regularization theorem and Kawashima's relation for multiple zeta values

Abstract

Kawashima's relation is conjecturally one of the largest classes of relations among multiple zeta values. Gaku Kawashima introduced and studied a certain Newton series, which we call the Kawashima function, and deduced his relation by establishing several properties of this function. We present a new approach to the Kawashima function without using Newton series. We first establish a generalization of the theory of regularizations of divergent multiple zeta values to Hurwitz type multiple zeta values, and then relate it to the Kawashima function. Via this connection, we can prove a key property of the Kawashima function to obtain Kawashima's relation.