On shuffle-type functional relations of desingularized multiple zeta-functions

Abstract

We treat desingularized multiple zeta-functions introduced by Furusho, Komori, Matsumoto and Tsumura. In this paper, we prove functional relations, which are shuffle type product formulae, between desingularized multiple zeta-functions and desingularized values.

Cyclic relation for multiple zeta functions

“…Hirose and the authors obtained some complex generalizations of known MZV relations such as "Sum formula" and "Ohno's relation" (see [3] and [4]). In addition, many studies have been conducted by various mathematicians to give functional relations (see [19], [24], [17], [18], [20], [15], [2], [5], [16], and [11], for example).…”