Products of weighted multiple zeta functions (Q1670378)

Multiple zeta functions satisfy the stuffle relation. For a formal power series \(f=\sum_{n\geq 1}a_nx^n\), the author defines the weighted multiple zeta function corresponding to \(f\). In this paper, the author characterizes all the weighted multiple zeta functions which satisfy the stuffle relations or the shuffle relations. The residues of the multiple zeta functions along some hyperplanes play important roles in establishing the main results.