Double Shuffle Relations for Multiple Dedekind Zeta Values

Abstract

This paper contains examples of shuffle relations among multiple Dedekind zeta values. Dedekind zeta values were defined by the author in his paper "Multiple Dedekind zeta functions". Here we concentrate on the cases of real or imaginary quadratic fields with up to double iteration. We give examples of integral shuffle relation in terms of iterated integrals over membranes and of infinite sum shuffle relation, sometimes called stuffle relation. Using both types of shuffles for the product $\zeta_{K,C}(2)\zeta_{K,C}(2)$, we find relations among multiple Dedekind zeta values for real and for imaginary quadratic fields.